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

Author

Amiram Eldar, Nov 09 2021

Keywords

• nonn
• more

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

Examples

			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.
		

Crossrefs

Cf. A002182, A339665, A348716.

Programs

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

Extensions

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