A241029 Sum of n-th powers of divisors of 22.

4, 36, 610, 11988, 248914, 5314716, 115151530, 2513845188, 55090232674, 1209627165996, 26585860217050, 584603613083988, 12858141059430034, 282844580595234876, 6222201023261420170, 136884245263581500388, 3011407446068928780994

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (36,-343,792,-484).

Formula

G.f.: 2*(2 - 54*x + 343*x^2 - 396*x^3)/((1 - x)*(1 - 2*x)*(1 - 11*x)*(1 - 22*x)). [Bruno Berselli, Apr 17 2014]

a(n) = (1 + 2^n)*(1 + 11^n). [Bruno Berselli, Apr 17 2014]

Mathematica

Total[#^Range[0, 20]&/@Divisors[22]]
Table[(1 + 2^n) (1 + 11^n), {n, 0, 20}] (* Bruno Berselli, Apr 17 2014 *)
LinearRecurrence[{36, -343, 792, -484}, {4, 36, 610, 11988}, 30] (* Harvey P. Dale, May 21 2014 *)

Prog

(Magma) [DivisorSigma(n, 22): n in [0..20]];
(Maxima) makelist((1+2^n)*(1+11^n), n, 0, 20); /* Bruno Berselli, Apr 17 2014 */

Crossrefs

Cf. sum of n-th powers of divisors of even k: A000051 (k=2), A001576 (k=4), A034488 (k=6), A034496 (k=8), A034517 (k=10), A034660 (k=12), A141013 (k=14), A020514 (k=16), A034661 (k=18), A034662 (k=20), this sequence (k=22), A034664 (k=24), A241030 (k=26), A241031 (k=28), A241032 (k=30), A034665 (k=32), A034666 (k=36), A034667 (k=40), A034668 (k=48), A034669 (k=56), A020516 (k=64), A034671 (k=72), A034672 (k=96), A034673 (k=120), A034674 (k=128), A034675 (k=144).

Sequence in context: A372241 A363010 A263445 * A002761 A002084 A374859

Adjacent sequences: A241026 A241027 A241028 * A241030 A241031 A241032

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 17 2014

Status

approved