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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
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
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
Sequence in context: A343574 A051821 A099031 * A205339 A215288 A295611
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 05 2001
STATUS
approved