A280195 Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).

1, 0, 1, 1, 2, 3, 4, 8, 11, 19, 28, 47, 72, 116, 182, 289, 460, 724, 1153, 1820, 2891, 4572, 7249, 11482, 18190, 28821, 45651, 72338, 114582, 181549, 287596, 455647, 721847, 1143588, 1811748, 2870239, 4547232, 7203907, 11412882, 18080833, 28644680, 45380392, 71894054, 113898439, 180443915, 285869028, 452888824, 717490903, 1136687237

Offset

0,5

Comments

Number of compositions (ordered partitions) into 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

Index entries for sequences related to compositions

Formula

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

Example

a(6) = 4 because we have [4, 2], [3, 3], [2, 4] and [2, 2, 2].

Mathematica

nmax = 48; CoefficientList[Series[1/(1 - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A001221, A023360, A023894, A246655.

Sequence in context: A135909 A046812 A269797 * A286224 A361313 A245388

Adjacent sequences: A280192 A280193 A280194 * A280196 A280197 A280198

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 28 2016

Status

approved