#!/usr/bin/env python
# -*- coding: utf-8 -*-
# ~ Jesse Rubin ~ project Euler ~
"""
Numbers with a given prime factor sum
http://projecteuler.net/problem=618
Consider the numbers 15, 16 and 18:
15=3× 5 and 3+5=8.
16 = 2× 2× 2× 2 and 2+2+2+2=8.
18 = 2× 3× 3 and 2+3+3=8.
15, 16 and 18 are the only numbers that have 8 as sum of the prime factors (counted with multiplicity).
We define S(k) to be the sum of all numbers n where the sum of the prime factors (with multiplicity)  of n is k.
Hence S(8) = 15+16+18 = 49.
Other examples: S(1) = 0, S(2) = 2, S(3) = 3, S(5) = 5 + 6 = 11.
The Fibonacci sequence is F_1 = 1, F_2 = 1, F_3 = 2, F_4 = 3, F_5 = 5, ....
Find the last nine digits of ∑_k=2^24S(F_k).
"""

def p618():
    pass

if __name__ == '__main__':
    p618()