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A281906 Expansion of Sum_{p prime, i>=1} p^i*x^(p^i)/(1 - x^(p^i)) / Product_{j>=1} (1 - x^j). 0
0, 2, 5, 13, 23, 41, 69, 119, 185, 283, 425, 625, 903, 1285, 1799, 2517, 3450, 4699, 6340, 8490, 11264, 14870, 19485, 25390, 32897, 42395, 54372, 69408, 88210, 111612, 140717, 176738, 221135, 275776, 342790, 424743, 524765, 646420, 794109, 972967, 1189105, 1449577, 1763097, 2139394, 2590349, 3129633, 3773546, 4540645 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Total sum of prime power parts (1 excluded) in all partitions of n.

Convolution of the sequences A000041 and A023889.

LINKS

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

Index entries for related partition-counting sequences

FORMULA

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

EXAMPLE

a(5) = 23 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 + 4 + 3 + 2 + 3 + 2 + 2 + 2 = 23.

MATHEMATICA

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

CROSSREFS

Cf. A000041, A023889, A066186, A073118, A246655.

Sequence in context: A102719 A075470 A049779 * A256491 A106009 A194552

Adjacent sequences: A281903 A281904 A281905 * A281907 A281908 A281909

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 01 2017

STATUS

approved

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Last modified November 29 10:31 EST 2022. Contains 358424 sequences. (Running on oeis4.)