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A017668 Denominator of sum of -2nd powers of divisors of n.

%I A017668 #26 Sep 08 2022 08:44:43
%S A017668 1,4,9,16,25,18,49,64,81,10,121,24,169,98,45,256,289,324,361,200,441,
%T A017668 242,529,288,625,338,729,56,841,9,961,1024,1089,578,49,432,1369,722,
%U A017668 1521,160,1681,441,1849,968,2025,1058,2209,1152,2401,500,2601,1352,2809
%N A017668 Denominator of sum of -2nd powers of divisors of n.
%C A017668 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
%H A017668 G. C. Greubel, <a href="/A017668/b017668.txt">Table of n, a(n) for n = 1..10000</a>
%H A017668 Colin Defant, <a href="https://arxiv.org/abs/1506.05432">On the Density of Ranges of Generalized Divisor Functions</a>, arXiv:1506.05432 [math.NT], 2015.
%F A017668 Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^2*(1 - x^k)). - _Ilya Gutkovskiy_, May 24 2018
%e A017668 1, 5/4, 10/9, 21/16, 26/25, 25/18, 50/49, 85/64, 91/81, 13/10, 122/121, 35/24, 170/169, ...
%t A017668 Table[Denominator[DivisorSigma[-2, n]], {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)
%t A017668 Table[Denominator[DivisorSigma[2, n]/n^2], {n, 1, 50}] (* _G. C. Greubel_, Nov 08 2018 *)
%o A017668 (PARI) a(n) = denominator(sigma(n, -2)); \\ _Michel Marcus_, Aug 24 2018
%o A017668 (PARI) vector(50, n, denominator(sigma(n, 2)/n^2)) \\ _G. C. Greubel_, Nov 08 2018
%o A017668 (Magma) [Denominator(DivisorSigma(2,n)/n^2): n in [1..50]]; // _G. C. Greubel_, Nov 08 2018
%Y A017668 Cf. A017667 (numerator).
%K A017668 nonn,frac
%O A017668 1,2
%A A017668 _N. J. A. Sloane_