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 A143773 Number of partitions of n such that every part is divisible by number of parts. 48
 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 5, 1, 4, 3, 6, 1, 8, 1, 7, 5, 6, 1, 14, 2, 7, 8, 11, 1, 17, 1, 14, 11, 9, 3, 29, 1, 10, 15, 23, 1, 28, 1, 23, 25, 12, 1, 51, 2, 20, 25, 32, 1, 44, 11, 39, 31, 15, 1, 94, 1, 16, 40, 52, 19, 64, 1, 57, 45, 44, 1, 126, 1, 19, 83, 74, 6, 90, 1, 124, 63, 21, 1, 186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 FORMULA G.f.: Sum(x^(k^2)/Product(1-x^(k*i), i=1..k), k=1..infinity). EXAMPLE The a(18) = 8 partitions are (18), (10 8), (12 6), (14 4), (16 2), (6 6 6), (9 6 3), (12 3 3). - Gus Wiseman, Jan 26 2018 MATHEMATICA m = 100; gf = Sum[x^(k^2)/Product[1-x^(k*i), {i, 1, k}], {k, 1, Sqrt[m]//Ceiling}]; CoefficientList[gf + O[x]^m, x] // Rest (* Jean-François Alcover, May 13 2019 *) PROG (PARI) Vec(sum(k=1, 20, x^(k^2)/prod(i=1, k, 1-x^(k*i)+O(x^400)))) \\ Max Alekseyev, May 03 2009 CROSSREFS Cf. A000005, A000041, A067538, A298422, A298423, A298426. Sequence in context: A305974 A332267 A161148 * A323524 A265893 A191372 Adjacent sequences:  A143770 A143771 A143772 * A143774 A143775 A143776 KEYWORD easy,nonn,look AUTHOR Vladeta Jovovic, Aug 31 2008 EXTENSIONS More terms from Max Alekseyev, May 03 2009 STATUS approved

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Last modified November 27 12:51 EST 2021. Contains 349394 sequences. (Running on oeis4.)