A034666 - OEIS

%I #29 Aug 04 2025 12:14:44

%S 9,91,1911,55261,1813539,62672701,2214363531,79017297541,

%T 2832604648419,101763873519661,3659794373013051,131686747008947221,

%U 4739547370427122899,170602660692644492221,6141318334706291980971

%N Sum of n-th powers of divisors of 36.

%H T. D. Noe, <a href="/A034666/b034666.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (91,-3185,57065,-580398,3482388,-12326040,24766560,-25474176,10077696).

%F G.f.: -(25474176*x^8 -49533120*x^7 +36978120*x^6 -13929552*x^5 +2901990*x^4 -342390*x^3 +22295*x^2 -728*x +9) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(6*x -1)*(9*x -1)*(12*x -1)*(18*x -1)*(36*x -1)). - _Colin Barker_, Apr 20 2014

%F From _Wesley Ivan Hurt_, Aug 04 2025: (Start)

%F a(n) = (1 + 2^n + 4^n) * (1 + 3^n + 9^n).

%F a(n) = 91*a(n-1) - 3185*a(n-2) + 57065*a(n-3) - 580398*a(n-4) + 3482388*a(n-5) - 12326040*a(n-6) + 24766560*a(n-7) - 25474176*a(n-8) + 10077696*a(n-9). (End)

%t Total[#^Range[0, 20]&/@Divisors[36]] (* _Vincenzo Librandi_, Apr 17 2014 *)

%t DivisorSigma[Range[0,20],36] (* _Harvey P. Dale_, Dec 23 2021 *)

%o (Magma) [DivisorSigma(n, 36): n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014

%Y Cf. A018256 (divisors of 36).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_