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
Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^5*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018
EXAMPLE
1, 33/32, 244/243, 1057/1024, 3126/3125, 671/648, 16808/16807, 33825/32768, 59293/59049, ...
MATHEMATICA
Table[Denominator[DivisorSigma[-5, n]], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
Table[Denominator[DivisorSigma[5, n]/n^5], {n, 1, 40}] (* G. C. Greubel, Nov 08 2018 *)
PROG
(PARI) vector(40, n, denominator(sigma(n, 5)/n^5)) \\ G. C. Greubel, Nov 08 2018
(Magma) [Denominator(DivisorSigma(5, n)/n^5): n in [1..40]]; // G. C. Greubel, Nov 08 2018
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
STATUS
approved