%I #8 Jun 17 2013 11:56:24

%S 3,17,29,49,45,111,37,115,109,159,69,319,45,207,279,191,69,367,69,487,

%T 315,183,93,681,141,235,291,495,117,909,53,357,331,259,559,967,45,279,

%U 459,949,117,1025,69,663,815,219,117,1205,161,591,411,555,93,965,579

%N Number of solutions (r,u,s,t) in positive integers to the system of equations 1/r + 1/u = 1/n, 1/s + 1/t = 1/u.

%F a(n) = Sum_{d|n^2} tau((n+d)^2).

%e For n=2 we have 17 solutions (r,u,s,t): (3,6,7,42), (3,6,8,24), (3,6,9,18), (3,6,10,15), (3,6,12,12), (3,6,15,10), (3,6,18,9), (3,6,24,8), (3,6,42,7), (4,4,5,20), (4,4,6,12), (4,4,8,8), (4,4,12,6), (4,4,20,5), (6,3,4,12), (6,3,6,6), (6,3,12,4).

%o (PARI) a(n) = sumdiv(n^2, d, numdiv((n+d)^2)) \\ _Michel Marcus_, Jun 17 2013

%Y Cf. A000005, A048691, A063716, A048691, A004194, A063520.

%K nonn

%O 1,1

%A _Vladeta Jovovic_, Aug 10 2001