A017700 Denominator of sum of -18th powers of divisors of n.

1, 262144, 387420489, 68719476736, 3814697265625, 50779978334208, 1628413597910449, 18014398509481984, 150094635296999121, 100000000000000000, 5559917313492231481, 4437222213480873984

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

Mathematica

Table[Denominator[Total[Divisors[n]^-18]], {n, 20}] (* Harvey P. Dale, Sep 25 2012 *)
Table[Denominator[DivisorSigma[18, n]/n^18], {n, 1, 20}] (* G. C. Greubel, Nov 05 2018 *)

Prog

(PARI) vector(20, n, denominator(sigma(n, 18)/n^18)) \\ G. C. Greubel, Nov 05 2018
(Magma) [Denominator(DivisorSigma(18, n)/n^18): n in [1..20]]; // G. C. Greubel, Nov 05 2018

Crossrefs

Cf. A017699.

Sequence in context: A016809 A018879 A016905 * A010806 A030637 A236226

Adjacent sequences: A017697 A017698 A017699 * A017701 A017702 A017703

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved