A335317 Harmonic numbers (A001599) with a record number of divisors.

1, 6, 28, 140, 270, 672, 2970, 8190, 30240, 332640, 2178540, 2457000, 11981970, 14303520, 17428320, 27027000, 163390500, 164989440, 191711520, 513513000, 1307124000, 2144862720, 2701389600, 3506025600, 5943057120, 13584130560, 14378364000, 29715285600, 45578332800

Offset

1,2

Comments

The corresponding record values are 1, 4, 6, 12, 16, 24, 32, 48, 96, ... (see the link for more values).

Links

Amiram Eldar, Table of n, a(n) for n = 1..40 (terms below 10^14)

Amiram Eldar, Table of n, a(n), A000005(a(n)) for n = 1..40

Example

The first 7 harmonic numbers are 1, 6, 28, 140, 270, 496 and 672. Their numbers of divisors (A000005) are 1, 4, 6, 12, 16, 10 and 24. The record values, 1, 4, 6, 12, 16 and 24 occur at 1, 6, 28, 140, 270 and 672, the first 6 terms of this sequence.

Mathematica

dm = 0; s = {}; Do[h = n * (d = DivisorSigma[0, n]) / DivisorSigma[1, n]; If[IntegerQ[h] && d > dm, dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s

Crossrefs

Cf. A000005, A001599, A335316, A335318.

Sequence in context: A199315 A001599 A335316 * A074247 A053783 A216383

Adjacent sequences: A335314 A335315 A335316 * A335318 A335319 A335320

Keyword

nonn

Author

Amiram Eldar, May 31 2020

Status

approved