Created harshad_numbers.py

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()

maths/harshad_numbers.py

@@ -0,0 +1,158 @@
+"""
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
+Reference: https://en.wikipedia.org/wiki/Harshad_number
+"""
+
+
+def int_to_base(number: int, base: int) -> str:
+ """
+ Convert a given positive decimal integer to base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> int_to_base(23, 2)
+ '10111'
+ >>> int_to_base(58, 5)
+ '213'
+ >>> int_to_base(167, 16)
+ 'A7'
+ >>> # bases below 2 and beyond 36 will error
+ >>> int_to_base(98, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> int_to_base(98, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ result = ""
+
+ if number < 0:
+ raise ValueError("number must be a positive integer")
+
+ while number > 0:
+ number, remainder = divmod(number, base)
+ result = digits[remainder] + result
+
+ if result == "":
+ result = "0"
+
+ return result
+
+
+def sum_of_digits(num: int, base: int) -> str:
+ """
+ Calculate the sum of digit values in a positive integer
+ converted to the given 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> sum_of_digits(103, 12)
+ '13'
+ >>> sum_of_digits(1275, 4)
+ '30'
+ >>> sum_of_digits(6645, 2)
+ '1001'
+ >>> # bases below 2 and beyond 36 will error
+ >>> sum_of_digits(543, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> sum_of_digits(543, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ num_str = int_to_base(num, base)
+ res = sum(int(char, base) for char in num_str)
+ res_str = int_to_base(res, base)
+ return res_str
+
+
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
+ """
+ Finds all Harshad numbers smaller than num in base 'base'.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> harshad_numbers_in_base(15, 2)
+ ['1', '10', '100', '110', '1000', '1010', '1100']
+ >>> harshad_numbers_in_base(12, 34)
+ ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+ >>> harshad_numbers_in_base(12, 4)
+ ['1', '2', '3', '10', '12', '20', '21']
+ >>> # bases below 2 and beyond 36 will error
+ >>> harshad_numbers_in_base(234, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> harshad_numbers_in_base(234, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if limit < 0:
+ return []
+
+ numbers = [
+ int_to_base(i, base)
+ for i in range(1, limit)
+ if i % int(sum_of_digits(i, base), base) == 0
+ ]
+
+ return numbers
+
+
+def is_harshad_number_in_base(num: int, base: int) -> bool:
+ """
+ Determines whether n in base 'base' is a harshad number.
+ Where 'base' ranges from 2 to 36.
+
+ Examples:
+ >>> is_harshad_number_in_base(18, 10)
+ True
+ >>> is_harshad_number_in_base(21, 10)
+ True
+ >>> is_harshad_number_in_base(-21, 5)
+ False
+ >>> # bases below 2 and beyond 36 will error
+ >>> is_harshad_number_in_base(45, 37)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ >>> is_harshad_number_in_base(45, 1)
+ Traceback (most recent call last):
+ ...
+ ValueError: 'base' must be between 2 and 36 inclusive
+ """
+
+ if base < 2 or base > 36:
+ raise ValueError("'base' must be between 2 and 36 inclusive")
+
+ if num < 0:
+ return False
+
+ n = int_to_base(num, base)
+ d = sum_of_digits(num, base)
+ return int(n, base) % int(d, base) == 0
+
+
+if __name__ == "__main__":
+ import doctest
+
+ doctest.testmod()