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 A066108 Sum n^d over all divisors of n. 8
 1, 6, 30, 276, 3130, 46914, 823550, 16781384, 387421227, 10000100110, 285311670622, 8916103456860, 302875106592266, 11112006930971730, 437893890381622140, 18446744078004584720, 827240261886336764194, 39346408075494930884190, 1978419655660313589123998 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is neither the Moebius transform nor the inverse Moebius transform of n^n, although it is close to them. LINKS Harry J. Smith, Table of n, a(n) for n = 1..100 FORMULA a(n) = Sum_{d|n} n^d. a(n) ~ n^n. - Vaclav Kotesovec, Jun 05 2021 EXAMPLE 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). MATHEMATICA Table[Sum[n^d, {d, Divisors@ n}], {n, 19}] (* Michael De Vlieger, Dec 20 2015 *) PROG (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 */ CROSSREFS Cf. A062793, A062796. Sequence in context: A343574 A051821 A099031 * A205339 A215288 A295611 Adjacent sequences: A066105 A066106 A066107 * A066109 A066110 A066111 KEYWORD nonn AUTHOR Labos Elemer, Dec 05 2001 STATUS approved

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Last modified August 9 20:51 EDT 2024. Contains 375044 sequences. (Running on oeis4.)