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%I A359112 #30 Aug 27 2023 17:03:24
%S A359112 1,3,4,13,6,109,8,777,2197,7541,12,374809,14,1675773,31954096,
%T A359112 100794385,18,7391871271,20,163547770441,2037381161992,570634875581,
%U A359112 24,1275177760626097,476837158203151,605750431288341,450286447756825720,2258377795760750777,30
%N A359112 a(n) = Sum_{d|n} (n/d) * d^(n-d).
%F A359112 G.f.: Sum_{k>=1} x^k/(1 - (k * x)^k)^2.
%F A359112 If p is prime, a(p) = 1 + p.
%t A359112 a[n_] := DivisorSum[n, #^(n-#)*n/# &]; Array[a, 29] (* _Amiram Eldar_, Aug 27 2023 *)
%o A359112 (PARI) a(n) = sumdiv(n, d, n/d*d^(n-d));
%o A359112 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)^2))
%Y A359112 Cf. A000203, A167531.
%Y A359112 Cf. A082245, A342628.
%K A359112 nonn
%O A359112 1,2
%A A359112 _Seiichi Manyama_, Dec 17 2022

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