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%I #25 Sep 08 2022 08:44:52
%S 6,39,455,6813,112931,1956669,34591115,617285253,11064693731,
%T 198756808749,3574014537275,64300154115093,1157115988280531,
%U 20825519793796029,374836322743499435,6746846977808919333
%N Sum of n-th powers of divisors of 18.
%H T. D. Noe, <a href="/A034661/b034661.txt">Table of n, a(n) for n=0..200</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (39,-533,3285,-9594,12636,-5832).
%F From _Philippe Deléham_, Apr 04 2013: (Start)
%F G.f.: 1/(1-x) + 1/(1-2*x) + 1/(1-3*x) + 1/(1-6*x) + 1/(1-9*x) + 1/(1-18*x).
%F a(n) = A000051(n)*A034513(n) = (2^n+1)*(3^n+9^n+1).
%F a(n) = 39*a(n-1) -533*a(n-2) +3285*a(n-3) -9594*a(n-4) +12636*a(n-5) -5832*a(n-6) with n>6, a(0)=6, a(1)=39, a(2)=455, a(3)=6813, a(4)= 112931, a(5)=1956669, a(6)=34591115. (End)
%t Join[{6}, LinearRecurrence[{39, -533, 3285, -9594, 12636, -5832}, {39, 455, 6813, 112931, 1956669, 34591115}, 15]] (* _Bruno Berselli_, Apr 05 2013 *)
%t Table[(2^n + 1) (3^n + 9^n + 1), {n, 0, 15}] (* _Bruno Berselli_, Apr 05 2013 *)
%t Total[#^Range[0, 20]&/@Divisors[18]] (* _Vincenzo Librandi_, Apr 17 2014 *)
%o (Sage) [sigma(18,n)for n in range(0,16)] # [_Zerinvary Lajos_, Jun 04 2009]
%o (Magma) [DivisorSigma(n, 18): n in [0..20]]; // _Bruno Berselli_, Apr 05 2013 (improved MAGMA code by _Vincenzo Librandi_, Apr 17 2014)
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
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