fractions.py

from fractions import Fraction


def get_fractions(m=5):
    all_fractions = [Fraction(nume,deno) for deno in range(1,m+1) for nume in range(0,deno+1)]
    uniq_fractions = set(all_fractions)
    fractions_list = list(uniq_fractions)
    fractions_list.sort()
    return fractions_list

for i in range(10):
    print(get_fractions(i))

num_digits.py

from collections import Counter
import math

single_prime_digits = [2,3,5,7]


def factors(n):
    while n > 1:
        for i in single_prime_digits:
            if n % i == 0:
                n /= i
                yield i
                break
        else:
            break


def get_all_factors(x):
    return [m for m in factors(x)]

# for i in [360,100,1000,1,10]:
#     print(get_all_factors(i))


def get_numdigits(x):
    if x in [0,1]:
        return 1
    all_factors = get_all_factors(x)
    mul_num = 1
    for i in all_factors:
        mul_num*=i
    if mul_num!=x:
        return -1
    counts = Counter(get_all_factors(x))
    count_2 = math.ceil(counts[2]/3)
    count_3 = math.ceil(counts[3]/2)
    digit_count = counts[5]+counts[7]+count_2+count_3
    return digit_count

for i in [32,10**10+2]:
    print(i, get_numdigits(i))