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A349179
Numbers with a record number of nonempty subsets of divisors whose harmonic mean is an integer (A339665).
1
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
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Nov 09 2021
EXTENSIONS
a(20) from Chai Wah Wu, Nov 09 2021
STATUS
approved