%I #6 Aug 06 2015 20:55:06

%S 1,5,4,8,6,14,7,15,12,22,7,26,9,24,23,30,8,42,11,31,21,29,12,56,18,32,

%T 27,48,13,68,11,42,35,40,32,65,9,35,30,76,9,87,18,51,49,39,18,97,27,

%U 70,31,52,14,108,36,72,33,52,17,120,15,37,66,90,36,93,12,63,44,123,19,130

%N Sum divides product: number of integer solutions (w,x,y,z), w >= x >= y >= z > 0, to the equation w*x*y*z = n*(w+x+y+z).

%C See A063520 for the corresponding problem in three variables.

%e a(7) = 7, since there are seven such solutions to wxyz = 7(w+x+y+z): (42,2,2,2), (49,4,2,1), (7,4,4,1), (10,7,2,1), (70,8,1,1), (28,10,1,1) and (16,14,1,1).

%o (PARI) A065015(n,d=0)={sum(x=1,sqrtn(4*n+.5,3),sum(y=x,sqrtint(4*n\x),sum(z=max(y,n\(x*y)+1),4*n\(x*y),(x+y+z)*n%(x*y*z-n)==0&&(x+y+z)*n>=(x*y*z-n)*z&&!(d&&print1([x,y,z,t=(x+y+z)*n/(x*y*z-n),x*y*z*t/(x+y+z+t)])))))} \\ _M. F. Hasler_, Aug 01 2015

%Y Cf. A063520, A071690.

%K nonn

%O 1,2

%A _John W. Layman_, Nov 01 2001