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

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2016

Keywords

• nonn

Comments

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

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Prime Power

Crossrefs

Cf. A001221, A098238, A246655.

Programs

Mathematica

nmax = 70; CoefficientList[Series[(Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}])^3, {x, 0, nmax}], x]

Formula

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