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

0,8

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].

Mathematica

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

Crossrefs

Cf. A001221, A098238, A246655.

Sequence in context: A187744 A007960 A339213 * A032732 A187352 A310044

Adjacent sequences: A280240 A280241 A280242 * A280244 A280245 A280246

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2016

Status

approved