A034488 Sum of n-th powers of divisors of 6.

4, 12, 50, 252, 1394, 8052, 47450, 282252, 1686434, 10097892, 60526250, 362976252, 2177317874, 13062296532, 78368963450, 470199366252, 2821153019714, 16926788715972, 101560344351050, 609360902796252, 3656161927895954, 21936961102828212

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 (12,-47,72,-36).

Formula

a(n) = 1^n + 2^n + 3^n + 6^n.

G.f.: -2*(36*x^3 - 47*x^2 + 18*x - 2) / ((x - 1)*(2*x - 1)*(3*x - 1)*(6*x - 1)). - Colin Barker, Apr 20 2014

Mathematica

a[n_] := (2^n + 1)*(3^n + 1); Table[a[n], {n, 0, 19}] (* Zerinvary Lajos, Mar 25 2007 *)
Total[#^Range[0, 20]&/@Divisors[6]] (* Vincenzo Librandi, Apr 17 2014 *)

Prog

(Sage) [sigma(6, n)for n in range(0, 20)] # Zerinvary Lajos, Jun 04 2009
(PARI) a(n)=6^n+3^n+2^n+1 \\ Charles R Greathouse IV, Apr 28, 2011
(Magma) [DivisorSigma(n, 6): n in [0..20]]; // Vincenzo Librandi, Apr 17 2014

Crossrefs

Sequence in context: A149395 A149396 A149397 * A149398 A149399 A149400

Adjacent sequences: A034485 A034486 A034487 * A034489 A034490 A034491

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Apr 20 2014

Status

approved