A380749
a(n) is the number of positive integer solutions of n*x*y*z*w = (x + n) * (y + n) * (z + n) * (w + n), x <= y <= z <= w.
Original entry on oeis.org
0, 374, 450, 375, 301, 478, 228, 359, 238, 515, 206, 879, 259, 506, 780, 349, 284, 762, 135, 916, 905, 493, 99, 1189, 423, 306, 318, 869, 70, 1879, 97, 311, 714, 250, 778, 1300, 109, 258, 483, 1334, 71, 1987, 93, 545, 1451, 303, 64, 1156, 202, 504, 481, 822, 71
Offset: 1
For n=5, a(5) = 301 because 5*x*y*z*w = (x + 5)*(y + 5)*(z + 5)*(w + 5), 0 < x <= y <= z <= w has 301 positive integer solutions: {{2,12,596,357595}, {2,12,597,179095}, {2,12,598,119595}, ..., {6,7,9,220}, {6,10,11,20}, {7,9,10,20}}.
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Table[Length@Solve[n*x*y*z*w == (x + n) (y + n) (z + n) (w + n) &&
0 < x <= y <= z <= w, {x, y, z, w}, Integers], {n, 10}]
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.
Original entry on oeis.org
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
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}}.
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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}]
Showing 1-2 of 2 results.