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A359103 a(n) = Sum_{d|n} d * (n/d)^d.

%I A359103 #30 Aug 27 2023 17:03:25
%S A359103 1,4,6,16,10,54,14,112,99,230,22,996,26,1022,1620,3232,34,9828,38,
%T A359103 18100,16380,22814,46,133272,15675,106886,179388,354116,58,1218150,62,
%U A359103 1589824,1952676,2228870,630980,13767264,74,9962270,20732868,34787000,82,113676402,86
%N A359103 a(n) = Sum_{d|n} d * (n/d)^d.
%H A359103 Seiichi Manyama, <a href="/A359103/b359103.txt">Table of n, a(n) for n = 1..5000</a>
%F A359103 a(n) = n * A087909(n).
%F A359103 G.f.: Sum_{k>=1} k * x^k/(1 - k * x^k)^2.
%F A359103 If p is prime, a(p) = 2 * p.
%F A359103 a(n) = [x^n] Sum_{k>0} k * (n * x / k)^k / (1 - x^k). - _Seiichi Manyama_, Jan 16 2023
%t A359103 a[n_] := DivisorSum[n, (n/#)^#*# &]; Array[a, 43] (* _Amiram Eldar_, Aug 27 2023 *)
%o A359103 (PARI) a(n) = sumdiv(n, d, d*(n/d)^d);
%o A359103 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^2))
%Y A359103 Cf. A055225, A087909, A167531, A359112, A359863.
%K A359103 nonn
%O A359103 1,2
%A A359103 _Seiichi Manyama_, Dec 17 2022