OFFSET
1,4
COMMENTS
For this sequence, it does not matter whether singletons are considered pairwise coprime.
For n > 2, also the number of maximal pairwise coprime subsets of {2..n}.
For each prime p <= n, p divides exactly one element of each maximal subset. - Bert Dobbelaere, May 04 2021
LINKS
Bert Dobbelaere, Table of n, a(n) for n = 1..500
Bert Dobbelaere, Python program
EXAMPLE
The a(1) = 1 through a(9) = 7 subsets:
{1} {12} {123} {123} {1235} {156} {1567} {1567} {1567}
{134} {1345} {1235} {12357} {12357} {12357}
{1345} {13457} {13457} {12579}
{13578} {13457}
{13578}
{14579}
{15789}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@Most@*Subsets/@y];
Table[Length[fasmax[Select[Subsets[Range[n]], CoprimeQ@@#&]]], {n, 15}]
CROSSREFS
The case of pairs is A015614.
The case of triples is A015617.
The non-maximal version counting empty sets and singletons is A084422.
The non-maximal version counting singletons is A187106.
The version for indivisibility instead of coprimality is A326077.
The version for sets of divisors is A343652.
The version for sets of divisors > 1 is A343660.
A018892 counts coprime unordered pairs of divisors.
A051026 counts pairwise indivisible subsets of {1..n}.
A100565 counts pairwise coprime unordered triples of divisors.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2021
EXTENSIONS
More terms from Bert Dobbelaere, May 04 2021
STATUS
approved