A375787 - OEIS

%I #20 Nov 19 2024 00:40:47

%S 0,20,17,15,8,18,4,11,5,13,1,22,2,10,13,4,1,15,1,15,9,6,0,17,3,0,1,8,

%T 0,24,0,1,6,2,6,13,0,0,4,11,0,21,0,4,10,0,0,7,0,3,2,4,0,4,1,5,0,0,0,29

%N a(n) is the number of solutions of n*x*y*z = (x + n)*(y + n)*(z + n), 0 < x <= y <= z.

%C a(n) = 0 for primes n not less than 23.

%e For n=5, a(n) = 8 because 5*x*y*z = (x + 5)*(y + 5)*(z + 5), 0 < x <= y <= z has 8 integer solutions: {{2,12,595}, {2,14,95}, {2,15,70}, {2,20,35}, {3,6,220}, {3,10,20}, {4,5,45}, {5,5,20}}.

%t Table[{n, Length@Solve[n*x*y*z == (x + n) (y + n) (z + n) && 0 < x <= y <= z, {x, y, z}, Integers]}, {n, 60}][[All, 2]]

%Y Cf. A374059.

%K nonn,easy

%O 1,2

%A _Zhining Yang_, Oct 28 2024