A337559 Number of length three 1..n vectors that contain their harmonic mean.
1, 2, 3, 4, 5, 18, 19, 20, 21, 22, 23, 36, 37, 38, 51, 52, 53, 66, 67, 80, 81, 82, 83, 96, 97, 98, 99, 112, 113, 138, 139, 140, 141, 142, 155, 168, 169, 170, 171, 184, 185, 210, 211, 212, 237, 238, 239, 252, 253, 254, 255, 256, 257, 270, 271, 284, 285, 286, 287, 324, 325, 326, 339
Offset: 1
Keywords
Examples
For n = 1, the only solution is (1,1,1). For n = 6, the a(6) = 18 solutions are (k,k,k) for k=1,..,6, the 6 permutations of (2,3,6) and the 6 permutations of (3,4,6). For n = 40, the a(40)-a(39) = 13 new solutions are (40,40,40), the 6 permutations of (10,16,40) and the 6 permutations of (24,30,40).
Links
- Hywel Normington, Python code, 2020.
Formula
Empirical: If A174903(n) = 0, a(n) = a(n-1) + 1.
a(n)-a(n-1) = 1 (mod 6).