# Problem 578: Integers with decreasing prime powers
Any positive integer can be written as a product of prime powers:
p1a1 × p2a2 × ... × pkak, where pi are distinct prime integers,
ai > 0 and pi < pj if i < j. A decreasing prime power positive
integer is one for which ai ≥ aj if i < j. For example, 1, 2, 15=3×5,
360=23×32×5 and 1000=23×53 are decreasing prime power integers. Let C(n)
be the count of decreasing prime power positive integers not exceeding
n. C(100) = 94 since all positive integers not exceeding 100 have
decreasing prime powers except 18, 50, 54, 75, 90 and 98. You are given
C(106) = 922052. Find C(1013).