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

Author

N. J. A. Sloane

Keywords

• nonn
• frac

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

Crossrefs

Cf. A017699.

Programs

Magma

[Denominator(DivisorSigma(18,n)/n^18): n in [1..20]]; // G. C. Greubel, Nov 05 2018

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 *)

PARI

vector(20, n, denominator(sigma(n, 18)/n^18)) \\ G. C. Greubel, Nov 05 2018