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A089251
Number of elements e in all partitions of n such that e divides n.
2
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
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
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