A362802 -id:A362802 - cp's OEIS frontend

A362803 Indices of records in A362802.

Original entry on oeis.org

1, 6, 24, 48, 60, 84

Offset: 1

Amiram Eldar, May 04 2023

The corresponding record values are 0, 1, 4, 15, 175, 188, ... .

a(7) >= 120.

Cf. A348716, A349179, A362801, A362802.

A362801 Numbers whose set of divisors can be partitioned into disjoint parts, all of length > 1 and having integer harmonic mean.

Original entry on oeis.org

6, 12, 18, 24, 28, 30, 40, 42, 45, 48, 54, 56, 60, 66, 72, 78, 84, 90, 96, 102, 108, 112, 114, 120, 126, 132, 135, 138, 140, 144, 150, 156, 162, 168, 174, 180, 186, 192, 196, 198, 200, 204, 210, 216, 220, 222, 224, 225, 228, 234, 240, 246, 252, 258, 264, 270, 276

Offset: 1

Amiram Eldar, May 04 2023

nonn

Numbers k such that A362802(k) > 0.
Includes all the harmonic numbers (A001599) except for 1, since the set of their divisors has an integer harmonic mean (in this case the partition is into a single part).
This sequence is infinite. For example, if k is a term and p is a prime that does not divide k, then k*p is also a term.

			12 is a term since its set of divisors, {1, 2, 3, 4, 6, 12} can be partitioned into 2 disjoint parts, {1, 2, 3, 6} and {4, 12}, whose harmonic means, 2 and 6, are both integers.

Cf. A362802.

Subsequences: A001599 \ {1}, A348715, A362803 \ {1}.

harmQ[s_] := AllTrue[s, Length[#] > 1 && IntegerQ[HarmonicMean[#]] &]; q[n_] := Module[{d = Divisors[n], r}, r = ResourceFunction["SetPartitions"][d]; AnyTrue[r, harmQ]]; Do[If[q[n], Print[n]], {n, 1, 100}]

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A362803 Indices of records in A362802.

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A362801 Numbers whose set of divisors can be partitioned into disjoint parts, all of length > 1 and having integer harmonic mean.

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Mathematica