A309150 Number of solutions of the Diophantine equation 1/n + 1/x = 1/y + 1/z, where n >= 1, x > n, y > n and z > y.

0, 2, 7, 12, 20, 29, 27, 41, 52, 60, 48, 101, 51, 96, 134, 93, 62, 142, 71, 209, 176, 114, 79, 264, 134, 136, 176, 256, 99, 363, 88, 217, 262, 178, 368, 406, 100, 180, 311, 469, 119, 471, 113, 386, 508, 182, 116, 552, 223, 353

Offset

1,2

Links

Table of n, a(n) for n=1..50.

Example

n=2:  1/2 + 1/12 = 1/3 + 1/4, 1/2 + 1/30 = 1/3 + 1/5.

Mathematica

a[n_]:=Length@Solve[1/(n)+1/(x)==1/y+1/z&&x>n&&z>y&&y>n, {x, y, z}, Integers];
Array[a, 50]

Crossrefs

Cf. A309149, A063647, A018892.

Sequence in context: A133459 A023669 A137401 * A333354 A119713 A213041

Adjacent sequences: A309147 A309148 A309149 * A309151 A309152 A309153

Keyword

nonn

Author

S. Nazardonyavi, Jul 14 2019

Status

approved