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
From Amiram Eldar, Apr 02 2024: (Start)
Dirichlet g.f. of a(n)/A017676(n): zeta(s)*zeta(s+6).
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
KEYWORD
nonn,frac
AUTHOR
STATUS
approved