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A320426
Number of nonempty pairwise coprime subsets of {1,...,n}, where a single number is not considered to be pairwise coprime unless it is equal to 1.
15
1, 2, 5, 8, 19, 22, 49, 64, 95, 106, 221, 236, 483, 530, 601, 712, 1439, 1502, 3021, 3212, 3595, 3850, 7721, 7976, 11143, 11878, 14629, 15460, 30947, 31202, 62433, 69856, 76127, 80222, 89821, 91612, 183259, 192602, 208601, 214232, 428503, 431574, 863189
OFFSET
1,2
COMMENTS
Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1.
FORMULA
a(n) = A187106(n) - n + 1 = A084422(n) - n.
a(n) = A276187(n) + 1. - Gus Wiseman, May 08 2021
EXAMPLE
The a(4) = 8 subsets of {1,2,3,4} are {1}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,3,4}. - Michael B. Porter, Jan 12 2019
From Gus Wiseman, May 09 2021: (Start)
The a(2) = 2 through a(6) = 22 sets:
{1} {1} {1} {1} {1}
{1,2} {1,2} {1,2} {1,2} {1,2}
{1,3} {1,3} {1,3} {1,3}
{2,3} {1,4} {1,4} {1,4}
{1,2,3} {2,3} {1,5} {1,5}
{3,4} {2,3} {1,6}
{1,2,3} {2,5} {2,3}
{1,3,4} {3,4} {2,5}
{3,5} {3,4}
{4,5} {3,5}
{1,2,3} {4,5}
{1,2,5} {5,6}
{1,3,4} {1,2,3}
{1,3,5} {1,2,5}
{1,4,5} {1,3,4}
{2,3,5} {1,3,5}
{3,4,5} {1,4,5}
{1,2,3,5} {1,5,6}
{1,3,4,5} {2,3,5}
{3,4,5}
{1,2,3,5}
{1,3,4,5}
(End)
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], CoprimeQ@@#&]], {n, 10}]
CROSSREFS
The case of pairs is A015614.
The case with singletons is A187106.
The version without singletons (except {1}) is A276187.
Row sums of A320436.
The version for divisors > 1 is A343654.
The version for divisors without singletons is A343655.
The maximal version is A343659.
A018892 counts coprime unordered pairs of divisors.
A051026 counts pairwise indivisible subsets of {1...n}.
A087087 ranks pairwise coprime subsets of {1...n}.
A326675 ranks pairwise coprime non-singleton subsets of {1...n}.
Sequence in context: A197211 A256723 A032063 * A133147 A358828 A082630
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 08 2019
EXTENSIONS
a(25)-a(43) from Alois P. Heinz, Jan 08 2019
STATUS
approved