|
| |
|
|
A017675
|
|
Numerator of sum of -6th powers of divisors of n.
|
|
3
|
|
|
|
1, 65, 730, 4161, 15626, 23725, 117650, 266305, 532171, 101569, 1771562, 506255, 4826810, 3823625, 2281396, 17043521, 24137570, 34591115, 47045882, 32509893, 85884500, 57575765, 148035890, 97201325, 244156251, 12067025, 387952660, 244770825, 594823322
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Sum_{d|n} 1/d^k is equal to sigma_k(n)/n^k. So sequences A017665-A017712 also give the numerators and denominators of sigma_k(n)/n^k for k = 1..24. The power sums sigma_k(n) are in sequences A000203 (k=1), A001157-A001160 (k=2,3,4,5), A013954-A013972 for k = 6,7,...,24. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 05 2001
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 1..10000
|
|
|
FORMULA
|
Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k^6*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018
|
|
|
EXAMPLE
|
1, 65/64, 730/729, 4161/4096, 15626/15625, 23725/23328, 117650/117649, 266305/262144, ...
|
|
|
MATHEMATICA
|
A017675[n_Integer] := Numerator[DivisorSigma[-6, n]]; Table[A017675[n], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
Table[Numerator[DivisorSigma[6, n]/n^6], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *)
|
|
|
PROG
|
(PARI) vector(20, n, numerator(sigma(n, 6)/n^6)) \\ G. C. Greubel, Nov 07 2018
(MAGMA) [Numerator(DivisorSigma(6, n)/n^6): n in [1..20]]; // G. C. Greubel, Nov 07 2018
|
|
|
CROSSREFS
|
Cf. A017676.
Sequence in context: A088677 A321562 A034680 * A013954 A294301 A116277
Adjacent sequences: A017672 A017673 A017674 * A017676 A017677 A017678
|
|
|
KEYWORD
|
nonn,frac
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
