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

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

Programs

Magma

[DivisorSigma(n,21): n in [0..15]]; // Vincenzo Librandi, Apr 17 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 *)

PARI

s=[]; for(n=0, 30, s=concat(s, sigma(21, n))); s \\ Colin Barker, May 03 2014

Sage

[sigma(21,n)for n in range(0,16)] # Zerinvary Lajos, Jun 04 2009

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