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Search: id:A066108
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| A066108 |
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Sum n^d over all divisors of n. |
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+0
1
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| 1, 6, 30, 276, 3130, 46914, 823550, 16781384, 387421227, 10000100110, 285311670622, 8916103456860, 302875106592266, 11112006930971730, 437893890381622140, 18446744078004584720, 827240261886336764194
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is neither the Moebius transform nor the inverse Moebius transform of n^n, although it is close to them.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,100
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FORMULA
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a(n)=Apply[Plus, n^Divisors[n]]= Sum{n^d; d runs over divisors of n}.
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EXAMPLE
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n = 12: a(12) = A066106(12) = 8916103456860 = 8916100448256+2985984+20736+1728+144+12; For comparison: M-transform of n^n at 12 = 8916100401348 = 8916100448256-46656-256+0+4+0 = A062793(12); Inverse M-transform of n^n at 12 = 8916100495200 = 8916100448256+46656+256+27+4+1 = A062796(12);
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PROGRAM
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(PARI) { for (n=1, 100, d=divisors(n); a=sum(i=1, length(d), n^d[i]); write("b066108.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 15 2009]
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CROSSREFS
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Cf. A062793, A062796.
Sequence in context: A052585 A051821 A099031 this_sequence A110374 A111876 A119634
Adjacent sequences: A066105 A066106 A066107 this_sequence A066109 A066110 A066111
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KEYWORD
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nonn,new
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Dec 05 2001
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