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A034660 Sum of n-th powers of divisors of 12.

%I A034660 #27 Sep 08 2022 08:44:52
%S A034660 6,28,210,2044,22386,257908,3037530,36130444,431733666,5170140388,
%T A034660 61978939050,743375541244,8918294543346,107006334784468,
%U A034660 1283997101947770,15407492847694444,184887084343023426,2218628050709022148,26623434909949071690,319480609006403630044
%N A034660 Sum of n-th powers of divisors of 12.
%H A034660 T. D. Noe, <a href="/A034660/b034660.txt">Table of n, a(n) for n = 0..200</a>
%F A034660 G.f.: (6 - 140*x + 1148*x^2 - 4200*x^3 + 6888*x^4 - 4032*x^5)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-6*x)*(1-12*x)). - _Michael Somos_, Apr 02 2003
%t A034660 a[n_] := Plus@@(Divisors[12]^n)
%t A034660 Total[#^Range[0, 20]&/@Divisors[12]] (* _Vincenzo Librandi_, Apr 17 2014 *)
%t A034660 DivisorSigma[Range[0,20],12] (* _Harvey P. Dale_, Sep 17 2019 *)
%o A034660 (PARI) a(n)=if(n<0,0,polsym((x-1)*(x-2)*(x-3)*(x-4)*(x-6)*(x-12),n)[n+1])
%o A034660 (PARI) a(n)=if(n<0,0,1^n+2^n+3^n+4^n+6^n+12^n)
%o A034660 (Sage) [sigma(12,n)for n in range(0,17)] # _Zerinvary Lajos_, Jun 04 2009
%o A034660 (Magma) [&+[Divisors(12)[i]^n: i in [1..6]]: n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014
%o A034660 (Python)
%o A034660 def a(n): return sum(d**n for d in [1, 2, 3, 4, 6, 12])
%o A034660 print([a(n) for n in range(20)]) # _Michael S. Branicky_, Jun 28 2021
%K A034660 nonn,easy
%O A034660 0,1
%A A034660 _N. J. A. Sloane_