A349179 Numbers with a record number of nonempty subsets of divisors whose harmonic mean is an integer (A339665).

1, 2, 4, 6, 12, 18, 24, 30, 36, 48, 60, 120, 180, 240, 360, 720, 840, 1260, 1680, 2520

Offset

1,2

Comments

The corresponding record values are 1, 2, 3, 9, 17, 19, 37, 45, 57, 85, 301, 2416, 6813, 19925, 225498, 7461578, 27043615, 304505823, 3686045705, ...

A339665(2520) = 657929756646. - Chai Wah Wu, Nov 09 2021

Conjecture: a(n) = A002182(n-2) for n >= 9. - Chai Wah Wu, Nov 11 2021

Links

Table of n, a(n) for n=1..20.

Example

The first 4 terms of A339665 are  1, 2, 2 and 3. The record values, 1, 2 and 3, occur at 1, 2 and 4, the first 3 terms of this sequence.

Mathematica

c[n_] := Count[Subsets[Divisors[n]], _?(Length[#]>0 && IntegerQ[HarmonicMean[#]] &)]; cm = -1; s = {}; Do[If[(c1 = c[n]) > cm, cm = c1; AppendTo[s, n]], {n, 1, 240}]; s

Crossrefs

Cf. A002182, A339665, A348716.

Sequence in context: A167706 A331091 A072121 * A175305 A342702 A171923

Adjacent sequences: A349176 A349177 A349178 * A349180 A349181 A349182

Keyword

nonn,more

Author

Amiram Eldar, Nov 09 2021

Extensions

a(20) from Chai Wah Wu, Nov 09 2021

Status

approved