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A034661 Sum of n-th powers of divisors of 18. 3
6, 39, 455, 6813, 112931, 1956669, 34591115, 617285253, 11064693731, 198756808749, 3574014537275, 64300154115093, 1157115988280531, 20825519793796029, 374836322743499435, 6746846977808919333 (list; graph; refs; listen; history; text; internal format)
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: A252761 A145709 A280006 * A094654 A145001 A263955

Adjacent sequences:  A034658 A034659 A034660 * A034662 A034663 A034664

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)