A034663 Sum of n-th powers of divisors of 21.

4, 32, 500, 9632, 196964, 4101152, 85884500, 1801914272, 37828630724, 794320419872, 16680163512500, 350279478046112, 7355841353205284, 154472474629724192, 3243920610749364500, 68122323330527541152

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 (32,-262,672,-441).

Formula

a(n) = (1+3^n)*(1+7^n). - Bruno Berselli, Apr 17 2014

G.f.: -4*(168*x^3-131*x^2+24*x-1) / ((x-1)*(3*x-1)*(7*x-1)*(21*x-1)). - Colin Barker, May 03 2014

Mathematica

Total[#^Range[0, 20]&/@Divisors[21]] (* Vincenzo Librandi, Apr 17 2014 *)
Table[(1 + 3^n) (1 + 7^n), {n, 0, 20}] (* Bruno Berselli, Apr 17 2014 *)

Prog

(Sage) [sigma(21, n)for n in range(0, 16)] # Zerinvary Lajos, Jun 04 2009
(Magma) [DivisorSigma(n, 21): n in [0..15]]; // Vincenzo Librandi, Apr 17 2014
(PARI) s=[]; for(n=0, 30, s=concat(s, sigma(21, n))); s \\ Colin Barker, May 03 2014

Crossrefs

Sequence in context: A089285 A209197 A086906 * A192501 A192487 A093581

Adjacent sequences: A034660 A034661 A034662 * A034664 A034665 A034666

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved