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

1,2

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.

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

Example

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.

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

Crossrefs

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

Sequence in context: A108051 A199315 A001599 * A335317 A074247 A053783

Adjacent sequences: A335313 A335314 A335315 * A335317 A335318 A335319

Keyword

nonn

Author

Amiram Eldar, May 31 2020

Status

approved