A337560 Number of length four 1..n vectors that contain their harmonic mean.

1, 2, 3, 28, 29, 78, 79, 104, 105, 154, 155, 252, 253, 254, 351, 376, 377, 426, 427, 620, 717, 718, 719, 912, 913, 914, 915, 1084, 1085, 1374, 1375, 1400, 1425, 1426, 1619, 1812, 1813, 1814, 1839, 2128, 2129, 2442, 2443, 2564, 2829, 2830, 2831, 3192, 3193

Offset: 1

Author

Hywel Normington, Aug 31 2020

Keywords

• nonn

Examples

			For n = 1, the a(1) = 1 solution is (1,1,1,1).
For n = 4, the a(4) = 28 solutions are (k,k,k,k) for k=1,2,3,4, the 12 permutations of (1,2,4,4) and the 12 permutations of (2,3,4,4).
For n = 40, the a(40) - a(39) = 289 new solutions are:
  the 24 permutations of (4, 8, 10, 40),
  the 12 permutations of (4, 10, 40, 40),
  the 12 permutations of (5, 12, 40, 40),
  the 24 permutations of (8, 10, 12, 40),
  the 24 permutations of (8, 15, 20, 40),
  the 12 permutations of (10, 16, 16, 40),
  the 24 permutations of (10, 18, 24, 40),
  the 12 permutations of (10, 20, 40, 40),
  the 24 permutations of (12, 20, 24, 40),
  the 24 permutations of (14, 24, 35, 40),
  the 24 permutations of (15, 24, 30, 40),
  the 12 permutations of (16, 16, 20, 40),
  the 12 permutations of (20, 20, 24, 40),
  the 12 permutations of (20, 30, 40, 40),
  the 12 permutations of (24, 30, 30, 40),
  the 12 permutations of (28, 35, 40, 40),
  the 12 permutations of (30, 36, 40, 40),
  and (40, 40, 40, 40).
		

Links

• Hywel Normington, Python code, 2020.

Crossrefs

Cf. A248434, A337110, A337111, A337559.

Formula

a(n) - a(n-1) = 1 (mod 12).

Extensions

a(43)-a(49) from Alois P. Heinz, Feb 04 2023