A380750 a(n) is the smallest integer k such that k*x*y*z*w = (x + k) * (y + k) * (z + k) * (w + k), 0 < x <= y <= z <= w has exactly n integer solutions.
1019, 1559, 1637, 1103, 743, 419, 1039, 359, 311, 479, 653, 509, 389, 251, 593, 521, 263, 197, 1061, 131, 353, 269, 239, 167, 89, 179, 337, 113, 139, 83, 181, 229, 934, 898, 277, 151, 103, 554, 1042, 281, 109, 107, 566, 283, 1299, 79, 386, 157, 1959, 173, 241
Offset: 1
Keywords
Examples
For n=8, a(n)=359 because 359 is the smallest integer such that 359*x*y*z*w = (x+359)*(y+359)*(z+359)*(w+359), 0 < x <= y <= z <= w has exactly 8 positive integer solutions: {{2, 406, 6462, 209302385}, {3, 185, 30515, 357644416}, {4, 168, 1375, 1804333641}, {6, 74, 42001, 462553550}, {6, 97, 1406, 462553550}, {15, 28, 8600, 1804333641}, {15, 100, 168, 1804333641}, {22, 50, 234, 11057989441}}.
Links
- Zhining Yang, Table of n, a(n) for n = 1..171
Comments