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 A359863 a(n) = Sum_{d|n} d^(n/d) * (n/d)^d. 3

%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

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Last modified July 21 12:40 EDT 2024. Contains 374472 sequences. (Running on oeis4.)