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

Author

Ilya Gutkovskiy, Jan 05 2017

Keywords

• nonn

Comments

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

Examples

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

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

Crossrefs

Cf. A000961, A001221, A023893, A280195.

Programs

Mathematica

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

Formula

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