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Expansion of Sum_{k>0} (1/(1 - k*x^k)^2 - 1).
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%I #47 Jul 17 2023 00:59:27

%S 2,7,10,25,16,78,22,153,136,298,34,1254,40,1214,2004,3825,52,11385,58,

%T 20894,18932,25006,70,150002,18826,115274,199828,389510,88,1334624,94,

%U 1725281,2131188,2360266,725948,14878299,112,10486958,22329428,37317986,124,120957336,130

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

%F a(n) = Sum_{d|n} (n/d)^d * (d+1) = A055225(n) + A359103(n).

%F If p is prime, a(p) = 1 + 3*p.

%t a[n_] := DivisorSum[n, (n/#)^# * (# + 1) &]; Array[a, 50] (* _Amiram Eldar_, Jul 17 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (n/d)^d*(d+1));

%Y Cf. A338662, A363639, A363640.

%Y Cf. A007503, A055225, A359103, A363646.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Jun 13 2023