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

1,2

Links

Table of n, a(n) for n=1..63.

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).

Example

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).

Crossrefs

Cf. A248434, A337110, A337111, A337560.

Sequence in context: A305794 A317944 A145520 * A061412 A295317 A165646

Adjacent sequences: A337556 A337557 A337558 * A337560 A337561 A337562

Keyword

nonn

Author

Hywel Normington, Aug 31 2020

Status

approved