A335316 Harmonic numbers (A001599) with a record harmonic mean of divisors.

1, 6, 28, 140, 270, 672, 1638, 2970, 8190, 27846, 30240, 167400, 237510, 332640, 695520, 1421280, 2178540, 2457000, 11981970, 14303520, 17428320, 23963940, 27027000, 46683000, 56511000, 71253000, 142990848, 163390500, 164989440, 191711520, 400851360, 407386980

Offset: 1

Author

Amiram Eldar, May 31 2020

Keywords

• nonn

Comments

The corresponding record values are 1, 2, 3, 5, 6, 8, 9, 11, 15, ... (see the link for more values).

The terms 1, 6, 30240 and 332640 are also terms of A179971.

Examples

			The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their harmonic means of divisors (A001600) are 1, 2, 3, 5, 6, 5 and 8. The record values, 1, 2, 3, 5, 6 and 8 occur at 1, 6, 28, 140, 270 and 672, the first 6 terms of this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..70 (terms below 10^14)
• Amiram Eldar, Table of n, a(n), A099377(a(n)) for n = 1..70

Crossrefs

Cf. A001599, A001600, A099377, A099378, A179971, A335317, A335318.

Programs

Mathematica

h[n_] := n * DivisorSigma[0, n] / DivisorSigma[1, n]; hm = 0; s = {}; Do[h1 = h[n];  If[IntegerQ[h1] && h1 > hm, hm = h1; AppendTo[s, n]], {n, 1, 10^6}]; s