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

%I

%S 4,12,50,252,1394,8052,47450,282252,1686434,10097892,60526250,

%T 362976252,2177317874,13062296532,78368963450,470199366252,

%U 2821153019714,16926788715972,101560344351050,609360902796252,3656161927895954,21936961102828212

%N Sum of n-th powers of divisors of 6.

%H T. D. Noe, <a href="/A034488/b034488.txt">Table of n, a(n) for n=0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (12,-47,72,-36).

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

%F 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

%t a[n_] := (2^n + 1)*(3^n + 1); Table[a[n], {n, 0, 19}] (* _Zerinvary Lajos_, Mar 25 2007 *)

%t Total[#^Range[0, 20]&/@Divisors[6]] (* _Vincenzo Librandi_, Apr 17 2014 *)

%o (Sage) [sigma(6,n)for n in xrange(0,20)] # _Zerinvary Lajos_, Jun 04 2009

%o (PARI) a(n)=6^n+3^n+2^n+1 \\ _Charles R Greathouse IV_, Apr 28, 2011

%o (MAGMA) [DivisorSigma(n, 6): n in [0..20]]; // _Vincenzo Librandi_, Apr 17 2014

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Apr 20 2014

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Last modified November 16 22:05 EST 2019. Contains 329208 sequences. (Running on oeis4.)