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A343660
Number of maximal pairwise coprime sets of at least two divisors > 1 of n.
5
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 4, 0, 0, 1, 1, 1, 4, 0, 1, 1, 3, 0, 4, 0, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 8, 0, 1, 2, 0, 1, 4, 0, 2, 1, 4, 0, 6, 0, 1, 2, 2, 1, 4, 0, 4, 0, 1, 0, 8, 1, 1, 1
OFFSET
1,12
FORMULA
a(n) = A343652(n) - A005361(n).
EXAMPLE
The a(n) sets for n = 6, 12, 24, 30, 36, 60, 72, 96:
{2,3} {2,3} {2,3} {5,6} {2,3} {5,6} {2,3} {2,3}
{3,4} {3,4} {2,15} {2,9} {2,15} {2,9} {3,4}
{3,8} {3,10} {3,4} {3,10} {3,4} {3,8}
{2,3,5} {4,9} {3,20} {3,8} {3,16}
{4,15} {4,9} {3,32}
{5,12} {8,9}
{2,3,5}
{3,4,5}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@Most@*Subsets/@y];
Table[Length[fasmax[Select[Subsets[Rest[Divisors[n]]], CoprimeQ@@#&]]], {n, 100}]
CROSSREFS
The case of pairs is A089233.
The case with 1's is A343652.
The case with singletons is (also) A343652.
The non-maximal version is A343653.
The non-maximal version with 1's is A343655.
The version for subsets of {2..n} is A343659 (for n > 2).
A018892 counts coprime unordered pairs of divisors.
A051026 counts pairwise indivisible subsets of {1..n}.
A066620 counts pairwise coprime 3-sets of divisors.
A100565 counts pairwise coprime unordered triples of divisors.
Sequence in context: A345446 A354911 A367098 * A319058 A281116 A335447
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 26 2021
STATUS
approved