test.py

#!/usr/bin/env python

# The Expat License
#
# Copyright (c) 2020, Shlomi Fish
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
# SOFTWARE.

# import itertools
import sys
# import math

import primesieve


def calc_sum(MAX):
    sqmax = int(pow(MAX, 1.0/3.0)+1)
    arr = primesieve.primes(sqmax)
    ret = [MAX]

    q = {(0, 1)}

    while q:
        i, prod = q.pop()
        if i == len(arr):
            if prod > 1:
                ret.append(MAX // prod)
            continue
        if prod > MAX:
            continue
        p = arr[i]
        newprod = prod * p ** 3
        if newprod > MAX:
            if prod > 1:
                ret.append(MAX // prod)
            continue
        q.add((i + 1, prod))
        while newprod <= MAX:
            q.add((i + 1, newprod))
            newprod *= p

    return sum(ret)


def compare(got, expected, blurb):
    if got != expected:
        print('blurb =', blurb, 'got =', got, 'expected =', expected)
    assert got == expected


def main():
    compare(calc_sum(16), 19, '16')
    compare(calc_sum(100), 126, '100')
    compare(calc_sum(10000), 13344, '10000')
    result = calc_sum(10**18)
    print('Result =', result)


if __name__ == "__main__":
    main()