A309149 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, 3, 9, 14, 22, 33, 29, 44, 56, 65, 50, 108, 53, 101, 141, 97, 64, 150, 73, 216, 184, 119, 81, 274, 138, 141, 182, 263, 101, 378, 90, 222, 270, 183, 375, 419, 102, 185, 319, 479, 121, 486, 115, 394, 520, 187, 118, 565, 227, 362

Offset

1,2

Links

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

Example

n=2: 1/2 + 1/6 = 1/3 + 1/3, 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. A309150, A063647, A018892.

Sequence in context: A001968 A305373 A111907 * A294480 A195972 A274435

Adjacent sequences: A309146 A309147 A309148 * A309150 A309151 A309152

Keyword

nonn

Author

S. Nazardonyavi, Jul 14 2019

Status

approved