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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 (list; graph; refs; listen; history; text; internal format)
 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: A250298 A260224 A105071 * A147568 A006794 A032457 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

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Last modified April 14 05:00 EDT 2021. Contains 342941 sequences. (Running on oeis4.)