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

Author

Ilya Gutkovskiy, Dec 28 2016

Keywords

• nonn

Comments

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

Examples

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

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. A001221, A023360, A023894, A246655.

Programs

Mathematica

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

Formula

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