maths.special_numbers.harshad_numbers

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

Functions

harshad_numbers_in_base(→ list[str])

Finds all Harshad numbers smaller than num in base 'base'.

int_to_base(→ str)

Convert a given positive decimal integer to base 'base'.

is_harshad_number_in_base(→ bool)

Determines whether n in base 'base' is a harshad number.

sum_of_digits(→ str)

Calculate the sum of digit values in a positive integer

Module Contents

maths.special_numbers.harshad_numbers.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):

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ValueError: ‘base’ must be between 2 and 36 inclusive >>> harshad_numbers_in_base(234, 1) Traceback (most recent call last):

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ValueError: ‘base’ must be between 2 and 36 inclusive

maths.special_numbers.harshad_numbers.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):

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ValueError: ‘base’ must be between 2 and 36 inclusive >>> int_to_base(98, 37) Traceback (most recent call last):

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ValueError: ‘base’ must be between 2 and 36 inclusive

maths.special_numbers.harshad_numbers.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):

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ValueError: ‘base’ must be between 2 and 36 inclusive >>> is_harshad_number_in_base(45, 1) Traceback (most recent call last):

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ValueError: ‘base’ must be between 2 and 36 inclusive

maths.special_numbers.harshad_numbers.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):

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ValueError: ‘base’ must be between 2 and 36 inclusive >>> sum_of_digits(543, 37) Traceback (most recent call last):

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ValueError: ‘base’ must be between 2 and 36 inclusive