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Sum of n-th powers of divisors of 26.
2

%I #14 Sep 08 2022 08:46:07

%S 4,42,850,19782,485554,12252702,313742650,8094558822,209642795554,

%T 5440108178862,141304954146250,3672136647383862,95452254746808754,

%U 2481455748310337022,64513912079682866650,1677310528178740048902,43609408316038057305154

%N Sum of n-th powers of divisors of 26.

%H Vincenzo Librandi, <a href="/A241030/b241030.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (42,-457,1092,-676).

%F G.f.: 2*(2 - 63*x + 457*x^2 - 546*x^3)/((1 - x)*(1 - 2*x)*(1 - 13*x)*(1 - 26*x)).

%F a(n) = (1 + 2^n)*(1 + 13^n).

%t Total[#^Range[0, 20] & /@ Divisors[26]] (* or *) Table[(1 + 2^n) (1 + 13^n), {n, 0, 20}]

%o (Magma) [DivisorSigma(n, 26): n in [0..20]];

%Y Cf. similar sequences listed in A241029.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Apr 17 2014