

A335388


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


0



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



