A034666 Sum of n-th powers of divisors of 36.

9, 91, 1911, 55261, 1813539, 62672701, 2214363531, 79017297541, 2832604648419, 101763873519661, 3659794373013051, 131686747008947221, 4739547370427122899, 170602660692644492221, 6141318334706291980971

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (91,-3185,57065,-580398,3482388,-12326040,24766560,-25474176,10077696).

Crossrefs

Cf. A018256 (divisors of 36).

Programs

Magma

[DivisorSigma(n, 36): n in [0..20]]; // Vincenzo Librandi, Apr 17 2014

Mathematica

Total[#^Range[0, 20]&/@Divisors[36]] (* Vincenzo Librandi, Apr 17 2014 *)
DivisorSigma[Range[0,20],36] (* Harvey P. Dale, Dec 23 2021 *)

Formula

G.f.: -(25474176*x^8 -49533120*x^7 [phone]*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

From Wesley Ivan Hurt, Aug 04 2025: (Start)

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

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)