A280543 Expansion of 1/(1 - x - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).

1, 1, 2, 4, 8, 16, 31, 62, 123, 244, 483, 958, 1899, 3765, 7463, 14794, 29329, 58141, 115258, 228486, 452949, 897922, 1780031, 3528716, 6995293, 13867402, 27490602, 54497104, 108034531, 214166610, 424561814, 841647229, 1668473323, 3307565365, 6556885566, 12998306479, 25767716954, 51081672682

Offset

0,3

Comments

Number of compositions (ordered partitions) of n into prime powers (1 included).

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

Example

a(3) = 4 because we have [3], [2, 1], [1, 2] and [1, 1, 1].

Mathematica

nmax = 37; CoefficientList[Series[1/(1 - x - Sum[Floor[1/PrimeNu[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000961, A001221, A023893, A280195.

Sequence in context: A001591 A194628 A003240 * A282566 A251706 A251711

Adjacent sequences: A280540 A280541 A280542 * A280544 A280545 A280546

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 05 2017

Status

approved