# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a358660
Showing 1-1 of 1

%I A358660 #30 Aug 27 2023 17:02:12
%S A358660 1,4,12,76,630,7968,117656,2105416,43048917,1000781420,25937424612,
%T A358660 743130116112,23298085122494,793742455829456,29192926758107760,
%U A358660 1152930300766980112,48661191875666868498,2185915267189632382650,104127350297911241532860
%N A358660 a(n) = Sum_{d|n} d * (n/d)^(n-d).
%H A358660 Sidney Cadot, <a href="/A358660/b358660.txt">Table of n, a(n) for n = 1..100</a>
%F A358660 G.f.: Sum_{k>=1} k^(k-1) * x^k/(1 - k^(k-1) * x^k)^2.
%F A358660 If p is prime, a(p) = p + p^(p-1).
%t A358660 a[n_] := Total[Map[#*(n/#)^(n - #) &, Divisors[n]]];
%t A358660 Table[a[n],{n,1,100}]
%t A358660 a[n_] := DivisorSum[n, (n/#)^(n-#)*# &]; Array[a, 19] (* _Amiram Eldar_, Aug 27 2023 *)
%o A358660 (PARI) a(n) = sumdiv(n, d, d*(n/d)^(n-d));
%o A358660 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-k^(k-1)*x^k)^2))
%Y A358660 Cf. A090879, A342629, A356539, A359112.
%K A358660 nonn
%O A358660 1,2
%A A358660 _Seiichi Manyama_, Dec 17 2022

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE