A381644 a(n) is the number of positive integer solutions of n*x*y*z*v*w = (x + n) * (y + n) * (z + n) * (v + n) * (w + n), x <= y <= z <= v <= w.

0, 21313, 35472, 28901, 36366, 35534, 33048, 55548, 30891, 60741, 76106, 161909, 88494, 114437, 220621, 76856, 56832, 195942, 33510, 212618, 222606, 154046, 21700, 324700, 107022, 94149, 109693, 244884, 35992, 592482, 39051, 134282, 213723, 104829, 363935, 355519, 70334, 110560, 158300, 485946, 46982, 650655

Offset: 1

Author

Zhining Yang, Mar 03 2025

Keywords

• nonn

Examples

			For n=4, a(4) = 28901 because 4*x*y*z*v*w = (x + 4)*(y + 4)*(z + 4)*(v + 4)*(w + 4), 0 < x <= y <= z <= v <= w has 28901 positive integer solutions: {{2,13,205,42637,1818041676},{2,13,205,42638,909042156},{2,13,205,42639,606042316},{2,13,205,42640,454542396}, ..., {10, 10, 12, 14, 21}, {10, 11, 12, 14, 18}, {10, 12, 12, 14, 16}}.
		

Crossrefs

Cf. A374059, A375787, A380749, A380750.

Programs

Mathematica

Table[Length@Solve[n*x*y*z*v*w == (x + n)  (y + n)  (z + n) (v + n) (w + n) &&
    0 < x <= y <= z <= v <= w, {x, y, z, v, w}, Integers], {n, 8}]