Function harshad_numbers_in_base

maths/special_numbers/harshad_numbers.py:89–126

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',

(limit: int, base: int)

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
    >>> harshad_numbers_in_base(-12, 6)
    []
    """

    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: