A281905 Expansion of Sum_{i>=2} prime(i)*x^prime(i)/(1 - x^prime(i)) / Product_{j>=1} (1 - x^j).

0, 0, 3, 3, 11, 17, 35, 49, 84, 124, 199, 280, 426, 594, 858, 1172, 1654, 2224, 3061, 4066, 5472, 7196, 9543, 12391, 16196, 20857, 26921, 34351, 43924, 55574, 70419, 88455, 111142, 138697, 173025, 214527, 265895, 327831, 403825, 495234, 606755, 740371, 902507, 1096215, 1329912, 1608445, 1942926, 2340203

Offset

1,3

Comments

Total sum of odd prime parts in all partitions of n.

Convolution of the sequences A000041 and A005069.

Links

Table of n, a(n) for n=1..48.

Index entries for related partition-counting sequences

Formula

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

Example

a(5) = 11 because we have [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 5 + 3 + 3 = 11.

Mathematica

nmax = 48; Rest[CoefficientList[Series[Sum[Prime[i] x^Prime[i]/(1 - x^Prime[i]), {i, 2, nmax}]/Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A000041, A005069, A065091, A066186, A073118.

Sequence in context: A217712 A321678 A027416 * A347521 A278835 A163932

Adjacent sequences: A281902 A281903 A281904 * A281906 A281907 A281908

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2017

Status

approved