A374059 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.

1, 11, 13, 25, 7, 9, 22, 48, 5, 21, 14, 8, 280, 10, 1020, 4, 70, 3, 6, 240, 2, 42, 12, 660, 30

Offset: 0

Author

Zhining Yang, Oct 28 2024

Keywords

• nonn
• more

Comments

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

Examples

			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}}.
		

Crossrefs

Cf. A375787.

Extensions

a(12) corrected by Jinyuan Wang, Dec 04 2024