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Any positive integer can be written as a product of prime powers: p1a1 × p2a2 × ... × pkak,
where pi are distinct prime integers, ai &gt; 0 and pi &lt; pj if i &lt; j.
A decreasing prime power positive integer is one for which ai ≥ aj if i &lt; 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).

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