%I #22 Aug 09 2023 02:03:54
%S 1,4,6,24,10,156,14,528,747,1620,22,15000,26,12572,60780,98336,34,
%T 397908,38,1484840,1500324,495660,46,18514992,9765675,2768948,
%U 28697868,85098552,58,375843660,62,570425408,471565380,75759684,2626093820,7623165384,74,378536012
%N a(n) = Sum_{d|n} d^(n/d) * (n/d)^d.
%H Seiichi Manyama, <a href="/A359863/b359863.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = [x^n] Sum_{k>0} k * (n * x / k)^k / (1 - k * x^k).
%F If p is prime, a(p) = 2 * p.
%t a[n_] := DivisorSum[n, #^(n/#) * (n/#)^# &]; Array[a, 40] (* _Amiram Eldar_, Aug 09 2023 *)
%o (PARI) a(n) = sumdiv(n, d, d^(n/d)*(n/d)^d);
%Y Cf. A359004.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jan 16 2023