A280544 Expansion of 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k), where d(k) is the number of divisors (A000005).

1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 3, 0, 5, 2, 8, 3, 13, 5, 22, 10, 34, 18, 58, 31, 94, 57, 153, 99, 254, 172, 417, 302, 685, 523, 1136, 901, 1872, 1557, 3097, 2673, 5133, 4577, 8505, 7843, 14109, 13380, 23440, 22816, 38953, 38855, 64789, 66053, 107871, 112190, 179664, 190369, 299478, 322683, 499501, 546548

Offset: 0

Author

Ilya Gutkovskiy, Jan 05 2017

Keywords

• nonn

Comments

Number of compositions (ordered partitions) of n into composite parts (A002808).

Examples

			a(10) = 3 because we have [10], [6, 4] and [4, 6].
		

Links

• Eric Weisstein's World of Mathematics, Composite Number
• Index entries for sequences related to compositions

Crossrefs

Cf. A000005, A002808, A023360, A023895, A052284.

Programs

Mathematica

nmax = 59; CoefficientList[Series[1/(1 - Sum[(1 - Floor[2/DivisorSigma[0, k]]) x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

PARI

x='x+O('x^60); Vec(1/(1 - sum(k=2, 59, (1 - 2\numdiv(k))*x^k))) \\ Indranil Ghosh, Apr 03 2017

Formula

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