%I #23 Nov 05 2017 16:48:46
%S 1,9,28,129,126,1458,344,8705,20413,49394,1332,1104114,2198,2217546,
%T 16305408,33820673,4914,532253187,6860,2392632274,10500716072,
%U 8591716802,12168,422182489826,30517593751,549760658274,7625984925160
%N a(n) = Sum_{ d divides n } (n/d)^(3d).
%H Seiichi Manyama, <a href="/A073706/b073706.txt">Table of n, a(n) for n = 1..2096</a>
%F G.f.: Sum_{n>=1} -log(1 - (n^3)*x^n)/n = Sum_{n>=1} a(n) x^n/n.
%F G.f.: Sum_{k>=1} k^3*x^k/(1-k^3*x^k). - _Benoit Cloitre_, Apr 21 2003
%e a(10) = (10/1)^(3*1) +(10/2)^(3*2) +(10/5)^(3*5) +(10/10)^(3*10) = 49394 because positive divisors of 10 are 1, 2, 5, 10.
%t Table[Total[Quotient[n, x = Divisors[n]]^(3*x)], {n, 27}] (* _Jayanta Basu_, Jul 08 2013 *)
%Y Sum_{ d divides n } (n/d)^(k*d): A000005 (k=0), A055225 (k=1), A073705 (k=2), this sequence (k=3).
%K easy,nonn
%O 1,2
%A _Paul D. Hanna_, Aug 04 2002