A374059 - OEIS

%I #41 Dec 04 2024 09:12:41

%S 1,11,13,25,7,9,22,48,5,21,14,8,280,10,1020,4,70,3,6,240,2,42,12,660,

%T 30

%N a(n) is the smallest integer k such that k*x*y*z = (x + k) * (y + k) * (z + k), 0 < x <= y <= z has exactly n integer solutions.

%C a(27)=630, a(29)=60, a(30)=420. No solutions were found for n={25,26,28} with k<10^5.

%e For n=8, a(n)=5 because 5 is the smallest integer such that 5*x*y*z = (x+5)*(y+5)*(z+5), 0 < x <= y <= z has exactly 8 positive 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}}.

%Y Cf. A375787.

%K nonn,more

%O 0,2

%A _Zhining Yang_, Oct 28 2024

%E a(12) corrected by _Jinyuan Wang_, Dec 04 2024