This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A017670 #19 Sep 08 2022 08:44:43 %S A017670 1,8,27,64,125,6,343,512,729,500,1331,432,2197,343,375,4096,4913,648, %T A017670 6859,4000,1323,2662,12167,384,15625,8788,19683,2744,24389,125,29791, %U A017670 32768,3993,19652,6125,46656,50653,13718,59319,6400,68921,147,79507,21296,10125 %N A017670 Denominator of sum of -3rd powers of divisors of n. %C A017670 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 A017670 G. C. Greubel, <a href="/A017670/b017670.txt">Table of n, a(n) for n = 1..10000</a> %F A017670 Denominator of Sum_{d|n} 1/d^3. %F A017670 Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k^3*(1 - x^k)). - _Ilya Gutkovskiy_, May 24 2018 %e A017670 1, 9/8, 28/27, 73/64, 126/125, 7/6, 344/343, 585/512, 757/729, 567/500, 1332/1331, 511/432, ... %t A017670 Table[Denominator[DivisorSigma[-3, n]], {n, 50}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *) %t A017670 Table[Denominator[DivisorSigma[3, n]/n^3], {n, 1, 40}] (* _G. C. Greubel_, Nov 08 2018 *) %o A017670 (PARI) vector(40, n, denominator(sigma(n, 3)/n^3)) \\ _G. C. Greubel_, Nov 08 2018 %o A017670 (Magma) [Denominator(DivisorSigma(3,n)/n^3): n in [1..40]]; // _G. C. Greubel_, Nov 08 2018 %Y A017670 Cf. A017669. %K A017670 nonn,frac %O A017670 1,2 %A A017670 _N. J. A. Sloane_