A034661 Sum of n-th powers of divisors of 18.

6, 39, 455, 6813, 112931, 1956669, 34591115, 617285253, 11064693731, 198756808749, 3574014537275, 64300154115093, 1157115988280531, 20825519793796029, 374836322743499435, 6746846977808919333

Offset

0,1

Links

T. D. Noe, Table of n, a(n) for n=0..200

Index entries for linear recurrences with constant coefficients, signature (39,-533,3285,-9594,12636,-5832).

Formula

From Philippe Deléham, Apr 04 2013: (Start)

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).

a(n) = A000051(n)*A034513(n) = (2^n+1)*(3^n+9^n+1).

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)

Mathematica

Join[{6}, LinearRecurrence[{39, -533, 3285, -9594, 12636, -5832}, {39, 455, 6813, 112931, 1956669, 34591115}, 15]] (* Bruno Berselli, Apr 05 2013 *)
Table[(2^n + 1) (3^n + 9^n + 1), {n, 0, 15}] (* Bruno Berselli, Apr 05 2013 *)
Total[#^Range[0, 20]&/@Divisors[18]] (* Vincenzo Librandi, Apr 17 2014 *)

Prog

(Sage) [sigma(18, n)for n in range(0, 16)] # [Zerinvary Lajos, Jun 04 2009]
(Magma) [DivisorSigma(n, 18): n in [0..20]]; // Bruno Berselli, Apr 05 2013 (improved MAGMA code by Vincenzo Librandi, Apr 17 2014)

Crossrefs

Sequence in context: A145709 A280006 A336291 * A094654 A145001 A263955

Adjacent sequences: A034658 A034659 A034660 * A034662 A034663 A034664

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved