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Sum of n-th powers of divisors of 21.
2

%I #26 Sep 08 2022 08:44:52

%S 4,32,500,9632,196964,4101152,85884500,1801914272,37828630724,

%T 794320419872,16680163512500,350279478046112,7355841353205284,

%U 154472474629724192,3243920610749364500,68122323330527541152

%N Sum of n-th powers of divisors of 21.

%H T. D. Noe, <a href="/A034663/b034663.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 (32,-262,672,-441).

%F a(n) = (1+3^n)*(1+7^n). - _Bruno Berselli_, Apr 17 2014

%F 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

%t Total[#^Range[0, 20]&/@Divisors[21]] (* _Vincenzo Librandi_, Apr 17 2014 *)

%t Table[(1 + 3^n) (1 + 7^n), {n, 0, 20}] (* _Bruno Berselli_, Apr 17 2014 *)

%o (Sage) [sigma(21,n)for n in range(0,16)] # _Zerinvary Lajos_, Jun 04 2009

%o (Magma) [DivisorSigma(n,21): n in [0..15]]; // _Vincenzo Librandi_, Apr 17 2014

%o (PARI) s=[]; for(n=0, 30, s=concat(s, sigma(21, n))); s \\ _Colin Barker_, May 03 2014

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_.