

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
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OFFSET

1,4


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000


FORMULA

G.f.: Sum(x^(k^2)/Product(1x^(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[1x^(k*i), {i, 1, k}], {k, 1, Sqrt[m]//Ceiling}];
CoefficientList[gf + O[x]^m, x] // Rest (* JeanFrançois Alcover, May 13 2019 *)


PROG

(PARI) Vec(sum(k=1, 20, x^(k^2)/prod(i=1, k, 1x^(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



