A335388 Harmonic numbers (A001599) with a record number of divisors that are harmonic numbers.

1, 6, 140, 672, 30240, 332640, 2178540, 17428320, 163390500, 191711520, 326781000, 1307124000, 2701389600, 8104168800, 14378364000, 40520844000, 1175104476000, 7131668544000, 49921679808000

Offset

1,2

Comments

The corresponding record values are 1, 2, 3, 4, 7, 9, 12, 15, 17, 19, 21, 25, 29, 34, 35, 43, 54, 75, 84.

Links

Table of n, a(n) for n=1..19.

Example

1 has one divisor which is a harmonic number: 1. 6 has 2 divisors which are harmonic numbers: 1 and 6. The next harmonic number with more than 2 divisors which are harmonic numbers is 140 with 3 such divisors: 1, 28 and 140.

Mathematica

h = Cases[Import["https://oeis.org/A001599/b001599.txt", "Table"], {_, _}][[;; , 2]]; hQ[n_] := Divisible[n * DivisorSigma[0, n], DivisorSigma[1, n]]; hsigma[n_] := DivisorSum[n, Boole @ hQ[#] &]; hm = 0; s = {}; Do[h1 = hsigma[h[[k]]]; If[h1 > hm, hm = h1; AppendTo[s, h[[k]]]], {k, 1, Length[h]}]; s

Crossrefs

Cf. A001599, A335317.

Sequence in context: A342358 A122483 A335369 * A123729 A193835 A123728

Adjacent sequences: A335385 A335386 A335387 * A335389 A335390 A335391

Keyword

nonn,more

Author

Amiram Eldar, Jun 04 2020

Status

approved