login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A066108 Sum n^d over all divisors of n. 5
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 15:21 EDT 2021. Contains 345165 sequences. (Running on oeis4.)