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A343659
Number of maximal pairwise coprime subsets of {1..n}.
7
1, 1, 1, 2, 2, 3, 3, 4, 7, 9, 9, 10, 10, 12, 16, 19, 19, 20, 20, 22, 28, 32, 32, 33, 54, 61, 77, 84, 84, 85, 85, 94, 112, 123, 158, 161, 161, 176, 206, 212, 212, 214, 214, 229, 241, 260, 260, 263, 417, 428, 490, 521, 521, 526, 655, 674, 764, 818, 818, 820, 820, 874, 918, 975, 1182, 1189, 1189
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, 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 non-maximal version is A320426(n) = A276187(n) + 1.
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.
Sequence in context: A067619 A236972 A184351 * A146922 A283363 A236210
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2021
EXTENSIONS
More terms from Bert Dobbelaere, May 04 2021
STATUS
approved