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Numbers with a record number of nonempty subsets of divisors whose harmonic mean is an integer (A339665).
1

%I #12 Nov 12 2021 12:16:15

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

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

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

%C A339665(2520) = 657929756646. - _Chai Wah Wu_, Nov 09 2021

%C Conjecture: a(n) = A002182(n-2) for n >= 9. - _Chai Wah Wu_, Nov 11 2021

%e 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.

%t 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

%Y Cf. A002182, A339665, A348716.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Nov 09 2021

%E a(20) from _Chai Wah Wu_, Nov 09 2021