A089251 Number of elements e in all partitions of n such that e divides n.

1, 3, 5, 11, 13, 32, 31, 71, 83, 147, 140, 364, 273, 550, 681, 1108, 916, 2157, 1598, 3604, 3549, 5102, 4509, 11548, 8192, 13514, 15199, 24911, 18461, 45062, 28630, 59662, 56544, 78484, 79350, 167219, 99134, 175771, 189108, 331455, 215309

Offset

1,2

Links

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

Formula

Sum_{d|n} Sum_{k=1..d} A000041(n-n*k/d). - Vladeta Jovovic, Mar 23 2005

a(n) = sum_{d | n} A066633(n, d). - David Wasserman, Aug 31 2005

Example

For n = 4 the partitions of 4 are 3+1, 2+2, 2+1+1, 1+1+1+1. There are 12 elements in total of which only the part of size 3 does not divide 4, so a(4) = 12 - 1 = 11.

Maple

with(numtheory): with(combinat):
a:= n-> add(add(numbpart(n-n*k/d), k=1..d), d=divisors(n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Feb 07 2013

Mathematica

f[n_] := Block[{d = Divisors[n]}, Plus @@ Sum[ PartitionsP[n - n*k/d], {k, n}]]; Table[ f[n], {n, 36}] (* Robert G. Wilson v, Mar 24 2005 *)

Crossrefs

Sequence in context: A361575 A260224 A105071 * A147568 A359303 A006794

Adjacent sequences: A089248 A089249 A089250 * A089252 A089253 A089254

Keyword

nonn

Author

Jon Perry, Dec 12 2003

Extensions

More terms from David Wasserman, Aug 31 2005

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

Status

approved