

A168659


Number of partitions of n such that the number of parts is divisible by the greatest part. Also number of partitions of n such that the greatest part is divisible by the number of parts.


3



1, 1, 2, 2, 3, 3, 6, 6, 8, 9, 14, 16, 22, 25, 33, 39, 51, 60, 79, 92, 116, 137, 174, 204, 254, 300, 368, 435, 530, 625, 760, 896, 1076, 1267, 1518, 1780, 2121, 2484, 2946, 3444, 4070, 4749, 5594, 6514, 7637, 8879, 10384, 12043, 14040, 16255
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OFFSET

1,3


LINKS

Vladeta Jovovic, Table of n, a(n) for n=1..301 [bfile corrected by N. J. A. Sloane, Oct 05 2010]


EXAMPLE

a(5)=3 because in the partitions [1,1,1,1,1], [1,1,1,2], [1,1,3] the number of parts is divisible by the greatest part; not true for the partitions [1,2,2],[2,3], [1,4], and [5].  Emeric Deutsch, Dec 04 2009


MAPLE

a := proc (n) local pn, ct, j: with(combinat): pn := partition(n): ct := 0: for j to numbpart(n) do if `mod`(nops(pn[j]), max(seq(pn[j][i], i = 1 .. nops(pn[j])))) = 0 then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 50); # Emeric Deutsch, Dec 04 2009


CROSSREFS

Cf. A168656, A168657, A079501, A168655.
Sequence in context: A147795 A258186 A038716 * A035642 A213332 A133392
Adjacent sequences: A168656 A168657 A168658 * A168660 A168661 A168662


KEYWORD

nonn


AUTHOR

Vladeta Jovovic, Dec 02 2009


EXTENSIONS

Extended by Emeric Deutsch, Dec 04 2009


STATUS

approved



