%I #19 Aug 14 2023 01:59:57

%S 1,5,28,265,3126,46754,823544,16778273,387420733,10000015690,

%T 285311670612,8916100733146,302875106592254,11112006831323074,

%U 437893890380939688,18446744073843786241,827240261886336764178,39346408075300026047027

%N a(n) = Sum_{d|n} d^(d + n/d - 1).

%H Seiichi Manyama, <a href="/A359700/b359700.txt">Table of n, a(n) for n = 1..386</a>

%F G.f.: Sum_{k>0} (k * x)^k / (1 - k * x^k).

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

%t a[n_] := DivisorSum[n, #^(# + n/# - 1) &]; Array[a, 20] (* _Amiram Eldar_, Aug 14 2023 *)

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k*x^k)))

%Y Cf. A014566, A055225, A087909, A294956, A353013, A353014.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 11 2023