A017688 Denominator of sum of -12th powers of divisors of n.

1, 4096, 531441, 16777216, 244140625, 1088391168, 13841287201, 68719476736, 282429536481, 500000000000, 3138428376721, 1486016741376, 23298085122481, 28346956187648, 129746337890625, 281474976710656

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. A017687.

Programs

Magma

[Denominator(DivisorSigma(12,n)/n^12): n in [1..20]]; // G. C. Greubel, Nov 06 2018

Mathematica

Array[Denominator[Total[Divisors[#]^-12]]&,20] (* Harvey P. Dale, Dec 06 2012 *)
Table[Denominator[DivisorSigma[12, n]/n^12], {n, 1, 20}] (* G. C. Greubel, Nov 06 2018 *)

PARI

vector(20, n, denominator(sigma(n, 12)/n^12)) \\ G. C. Greubel, Nov 06 2018