A362802 a(n) is the number of ways in which the set of divisors of n can be partitioned into disjoint parts, all of length > 1 and with integer harmonic mean.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 15, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 175, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 188, 0

Offset

1,24

Links

Table of n, a(n) for n=1..85.

Formula

a(A362801(n)) > 0.

Example

 n  a(n)  partitions
==  ====  ==========
 6     1  {{1, 2, 3, 6}}
12     1  {{1, 2, 3, 6}, {4, 12}}
24     4  {{1, 2, 3, 6}, {4, 8, 12, 24}}, {{1, 2, 4, 8, 12, 24}, {3, 6}},
          {{1, 3, 6}, {2, 4, 8, 12, 24}}, {{1, 2, 3, 6}, {4, 12}, {8, 24}}

Mathematica

harmQ[s_] := AllTrue[s, Length[#] > 1 && IntegerQ[HarmonicMean[#]] &]; a[n_] := Module[{d = Divisors[n], r}, r = ResourceFunction["SetPartitions"][d]; Count[r, _?harmQ]]; Array[a, 119]

Crossrefs

Cf. A339453, A339665, A362801, A362803 (indices of records).

Sequence in context: A228368 A267701 A128975 * A245817 A343316 A277115

Adjacent sequences: A362799 A362800 A362801 * A362803 A362804 A362805

Keyword

nonn

Author

Amiram Eldar, May 04 2023

Status

approved