A382672 Number of integer solutions to Product_{k=1..n} (3 + c(k)) = 3 * Product_{k=1..n} c(k) with 0 < c(k) <= c(k+1).

0, 2, 17, 450, 35472, 12127741

Offset: 1

Author

Zhining Yang, Apr 03 2025

Keywords

• nonn
• more

Examples

			For n=3, a(3) = 17 because 3*x*y*z = (x + 3)*(y + 3)*(z + 3), 0 < x <= y <= z has 17 positive integer solutions: {{2,16,285}, {2,17,150}, {2,18,105}, {2,20,69}, {2,21,60}, {2,24,45}, {2,25,42}, {2,30,33}, {3,7,60}, {3,8,33}, {3,9,24}, {3,12,15}, {4,5,42}, {4,6,21}, {4,7,15}, {5,6,12}, {6,6,9}}.
		

Crossrefs

Cf. A263207, A375787, A380749, A381644.

Programs

Mathematica

a[n_]:=(p=c/@Range[n];Length@Solve[3 Times@@p==Times@@(3+p)&&LessEqual@@Flatten[{0,p}],p,Integers]);Array[a,5]