A065015 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).

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, 27, 48, 13, 68, 11, 42, 35, 40, 32, 65, 9, 35, 30, 76, 9, 87, 18, 51, 49, 39, 18, 97, 27, 70, 31, 52, 14, 108, 36, 72, 33, 52, 17, 120, 15, 37, 66, 90, 36, 93, 12, 63, 44, 123, 19, 130

Offset

1,2

Comments

See A063520 for the corresponding problem in three variables.

Links

Table of n, a(n) for n=1..72.

Example

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).

Prog

(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

Crossrefs

Cf. A063520, A071690.

Sequence in context: A003672 A081818 A023848 * A334401 A295162 A002340

Adjacent sequences: A065012 A065013 A065014 * A065016 A065017 A065018

Keyword

nonn

Author

John W. Layman, Nov 01 2001

Status

approved