A280605 Expansion of 1/(1 - Sum_{p prime, k>=2} x^(p^k)).

1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 3, 2, 0, 0, 6, 5, 1, 0, 10, 10, 3, 0, 18, 23, 9, 2, 31, 46, 22, 6, 56, 94, 56, 19, 101, 184, 129, 50, 185, 364, 293, 134, 344, 708, 638, 332, 651, 1378, 1375, 805, 1265, 2665, 2901, 1878, 2503, 5161, 6057, 4306, 5061, 10005, 12488, 9653, 10384, 19461, 25556, 21319

Offset

0,9

Comments

Number of compositions (ordered partitions) of n into proper prime powers (A246547).

Links

Table of n, a(n) for n=0..67.

Eric Weisstein's World of Mathematics, Prime Power

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{p prime, k>=2} x^(p^k)).

Example

a(12) = 3 because we have [8, 4], [4, 8] and [4, 4, 4].

Mathematica

nmax = 67; CoefficientList[Series[1/(1 - Sum[Sign[PrimeOmega[k] - 1] Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

Prog

(PARI) x='x+O('x^68); Vec(1/(1 - sum(k=2, 67, sign(bigomega(k) - 1) * (1\omega(k)) * x^k))) \\ Indranil Ghosh, Apr 03 2017

Crossrefs

Cf. A246547, A280195, A280200, A280543, A280586.

Sequence in context: A294265 A130507 A281449 * A362427 A218253 A037872

Adjacent sequences: A280602 A280603 A280604 * A280606 A280607 A280608

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 06 2017

Status

approved