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A363641 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^2.

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%I A363641 #13 Jul 19 2023 02:20:06
%S A363641 0,1,2,4,4,10,6,20,14,42,10,127,12,206,132,512,16,1459,18,2655,1492,
%T A363641 5142,22,17795,524,24602,17540,59567,28,177776,30,274656,196884,
%U A363641 524322,20156,1901506,36,2359334,2125828,5682323,40,17453224,42,24641943,22948512,46137390,46
%N A363641 Expansion of Sum_{k>0} x^(2*k)/(1 - k*x^k)^2.
%F A363641 a(n) = Sum_{d|n} (n/d)^(d-2) * (d-1).
%F A363641 If p is prime, a(p) = p - 1.
%t A363641 a[n_] := DivisorSum[n, (n/#)^(#-2) * (#-1) &]; Array[a, 50] (* _Amiram Eldar_, Jul 18 2023 *)
%o A363641 (PARI) a(n) = sumdiv(n, d, (n/d)^(d-2)*(d-1));
%Y A363641 Cf. A167531, A362683.
%Y A363641 Cf. A363649.
%K A363641 nonn
%O A363641 1,3
%A A363641 _Seiichi Manyama_, Jun 13 2023