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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. 1

%I

%S 0,3,9,14,22,33,29,44,56,65,50,108,53,101,141,97,64,150,73,216,184,

%T 119,81,274,138,141,182,263,101,378,90,222,270,183,375,419,102,185,

%U 319,479,121,486,115,394,520,187,118,565,227,362

%N 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.

%e 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.

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

%t Array[a,50]

%Y Cf. A309150, A063647, A018892.

%K nonn

%O 1,2

%A _S. Nazardonyavi_, Jul 14 2019

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)