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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 September 12 05:07 EDT 2024. Contains 375842 sequences. (Running on oeis4.)