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A280243

Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^3, where omega(k) is the number of distinct prime factors (A001221).

0, 0, 0, 0, 0, 0, 1, 3, 6, 10, 12, 15, 19, 24, 30, 34, 36, 39, 45, 45, 51, 52, 57, 66, 67, 66, 69, 73, 75, 87, 81, 87, 93, 94, 99, 111, 111, 126, 129, 130, 123, 141, 126, 156, 138, 150, 132, 168, 145, 168, 153, 172, 165, 195, 156, 189, 171, 202, 177, 228, 165, 225, 183, 225, 186, 243, 177, 243, 204, 238, 198

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OFFSET

0,8

COMMENTS

Number of ordered ways of writing n as sum of three prime powers (1 excluded).

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Prime Power

FORMULA

G.f.: (Sum_{k>=2} floor(1/omega(k))*x^k)^3.

EXAMPLE

a(7) = 3 because we have [3, 2, 2], [2, 3, 2] and [2, 2, 3].