A017678 Denominator of sum of -7th powers of divisors of n.

1, 128, 2187, 16384, 78125, 23328, 823543, 2097152, 4782969, 5000000, 19487171, 8957952, 62748517, 13176688, 56953125, 268435456, 410338673, 204073344, 893871739, 640000000, 1801088541, 623589472

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

Examples

			1, 129/128, 2188/2187, 16513/16384, 78126/78125, 23521/23328, 823544/823543, 2113665/2097152, ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A017677.

Programs

Magma

[Denominator(DivisorSigma(7,n)/n^7): n in [1..20]]; // G. C. Greubel, Nov 07 2018

Mathematica

Table[Denominator[Total[Divisors[n]^-7]],{n,30}] (* Harvey P. Dale, Mar 21 2012 *)
Table[Denominator[DivisorSigma[7, n]/n^7], {n, 1, 20}] (* G. C. Greubel, Nov 07 2018 *)

PARI

vector(20, n, denominator(sigma(n, 7)/n^7)) \\ G. C. Greubel, Nov 07 2018

Formula

Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^7*(1 - x^k)). - Ilya Gutkovskiy, May 25 2018