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