OFFSET
1,2
EXAMPLE
The a(n) sets for n = 1, 2, 4, 6, 8, 12, 24, 30, 32, 36, 48:
{} {} {} {} {} {} {} {} {} {} {}
{2} {2} {2} {2} {2} {2} {2} {2} {2} {2}
{4} {3} {4} {3} {3} {3} {4} {3} {3}
{6} {8} {4} {4} {5} {8} {4} {4}
{2,3} {6} {6} {6} {16} {6} {6}
{12} {8} {10} {32} {9} {8}
{2,3} {12} {15} {12} {12}
{3,4} {24} {30} {18} {16}
{2,3} {2,3} {36} {24}
{3,4} {2,5} {2,3} {48}
{3,8} {3,5} {2,9} {2,3}
{5,6} {3,4} {3,4}
{2,15} {4,9} {3,8}
{3,10} {3,16}
{2,3,5}
MATHEMATICA
pwcop[y_]:=And@@(GCD@@#1==1&)/@Subsets[y, {2}];
Table[Length[Select[Subsets[Rest[Divisors[n]]], pwcop]], {n, 100}]
CROSSREFS
The version for partitions is A007359.
The version for subsets of {1..n} is A084422.
The case of pairs is A089233.
The version with 1's is A225520.
The maximal case is A343652.
The case without empty sets or singletons is A343653.
The maximal case without singletons is A343660.
A018892 counts pairwise coprime unordered pairs of divisors.
A051026 counts pairwise indivisible subsets of {1..n}.
A100565 counts pairwise coprime unordered triples of divisors.
A326077 counts maximal pairwise indivisible sets.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2021
STATUS
approved