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 A013960 #48 Oct 29 2023 02:37:09
%S A013960 1,4097,531442,16781313,244140626,2177317874,13841287202,68736258049,
%T A013960 282430067923,1000244144722,3138428376722,8918294543346,
%U A013960 23298085122482,56707753666594,129746582562692,281543712968705,582622237229762,1157115988280531,2213314919066162
%N A013960 a(n) = sigma_12(n), the sum of the 12th powers of the divisors of n.
%C A013960 If the canonical factorization of n into prime powers is the product of p^e(p) then sigma_k(n) = Product_p ((p^((e(p)+1)*k))-1)/(p^k-1).
%C A013960 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 A013960 Vincenzo Librandi, <a href="/A013960/b013960.txt">Table of n, a(n) for n = 1..1000</a>
%H A013960 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A013960 G.f.: Sum_{k>=1} k^12*x^k/(1-x^k). - _Benoit Cloitre_, Apr 21 2003
%F A013960 Dirichlet g.f.: zeta(s-12)*zeta(s). - _Ilya Gutkovskiy_, Sep 10 2016
%F A013960 From _Amiram Eldar_, Oct 29 2023: (Start)
%F A013960 Multiplicative with a(p^e) = (p^(12*e+12)-1)/(p^12-1).
%F A013960 Sum_{k=1..n} a(k) = zeta(13) * n^13 / 13 + O(n^14). (End)
%t A013960 DivisorSigma[12,Range[20]] (* _Harvey P. Dale_, Jan 28 2015 *)
%o A013960 (Sage) [sigma(n,12) for n in range(1,17)] # _Zerinvary Lajos_, Jun 04 2009
%o A013960 (Magma) [DivisorSigma(12, n): n in [1..20]]; // _Vincenzo Librandi_, Sep 10 2016
%o A013960 (PARI) my(N=99, q='q+O('q^N)); Vec(sum(n=1, N, n^12*q^n/(1-q^n))) \\ _Altug Alkan_, Sep 10 2016
%o A013960 (PARI) a(n) = sigma(n, 12); \\ _Amiram Eldar_, Oct 29 2023
%Y A013960 Cf. A000203, A001157-A001160, A013671, A013954-A013972, A017665-A017712.
%K A013960 nonn,mult,easy
%O A013960 1,2
%A A013960 _N. J. A. Sloane_