A281852 Expansion of Sum_{p prime, i>=1} x^(p^i) / (1 - Sum_{p prime, j>=1} x^(p^j))^2.

0, 1, 1, 3, 5, 9, 18, 29, 55, 91, 163, 274, 472, 798, 1349, 2275, 3804, 6380, 10614, 17685, 29318, 48584, 80296, 132506, 218329, 359139, 590092, 968120, 1586707, 2597349, 4247619, 6939353, 11326636, 18471726, 30099313, 49008929, 79739345, 129650164, 210661777, 342080831, 555153086, 900432434, 1459670289

Offset: 1

Author

Ilya Gutkovskiy, Jan 31 2017

Keywords

• nonn

Comments

Total number of parts in all compositions (ordered partitions) of n into prime powers (1 excluded).

Examples

			a(7) = 18 because we have [7], [5, 2], [4, 3], [3, 4], [3, 2, 2], [2, 5], [2, 3, 2], [2, 2, 3] and 1 + 2 + 2 + 2 + 3 + 2 + 3 + 3 = 18.
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A121304, A246655, A280195.

Programs

Mathematica

nmax = 43; Rest[CoefficientList[Series[Sum[Floor[1/PrimeNu[i]] x^i, {i, 2, nmax}]/(1 - Sum[Floor[1/PrimeNu[j]] x^j, {j, 2, nmax}])^2, {x, 0, nmax}], x]]

Formula

G.f.: Sum_{p prime, i>=1} x^(p^i) / (1 - Sum_{p prime, j>=1} x^(p^j))^2.