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Search: id:A089251
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| A089251 |
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Number of elements e in all partitions of n such that e divides n. |
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+0
1
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| 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
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OFFSET
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1,2
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FORMULA
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Sum_{d|n} Sum_{k=1..d} A000041(n-n*k/d). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 23 2005
a(n) = sum_{d | n} A066633(n, d). - David Wasserman (wasserma(AT)spawar.navy.mil), Aug 31 2005
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EXAMPLE
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a(4)=11 as partitions are 4,31,22,211,1111 - 12 elements in total of which only 3 does not divide 4.
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MATHEMATICA
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f[n_] := Block[{d = Divisors[n]}, Plus @@ Sum[ PartitionsP[n - n*k/d], {k, n}]]; Table[ f[n], {n, 36}] (from Robert G. Wilson v Mar 24 2005)
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CROSSREFS
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Sequence in context: A153075 A095082 A105071 this_sequence A147568 A006794 A032457
Adjacent sequences: A089248 A089249 A089250 this_sequence A089252 A089253 A089254
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Dec 12 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Aug 31 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar
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