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A066108
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Sum n^d over all divisors of n.
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8
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1, 6, 30, 276, 3130, 46914, 823550, 16781384, 387421227, 10000100110, 285311670622, 8916103456860, 302875106592266, 11112006930971730, 437893890381622140, 18446744078004584720, 827240261886336764194, 39346408075494930884190, 1978419655660313589123998
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OFFSET
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1,2
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COMMENTS
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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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FORMULA
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a(n) = Sum_{d|n} n^d.
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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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MATHEMATICA
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PROG
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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) ) } \\ Harry J. Smith, Nov 15 2009
(PARI) a(n)=sumdiv(n, d, n^d ); /* Joerg Arndt, Oct 07 2012 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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