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A018892 counts coprime unordered pairs of divisors.

A100565 counts pairwise coprime unordered triples of divisors.

Number of pairwise coprime sets of divisors of n, where a singleton is not considered pairwise coprime unless it is {1}.

Cf. A000005, A007360, A062319, A067824, A074206, A076078, A084422, A089233, A187106, A282935, `A285572, A304709, A320423, `A324837, A337485, `A337984, A343659.

The A version for prime indices is A304711.

Cf. A000005, A007360, A062319, A067824, A074206, A076078, A084422, A089233, A187106, A282935, `A285572, A304709, A320423, `A324837, ~A326674A337485, `A337984, A343659.

Cf. A067824, A074206.

Cf. `A007360, A084422, A089233, A187106, A304709, ~A307719, A320423, ~A337462, A337485, `A337984, A343659.

Cf. ~A326496.

Cf. `A062319.

allocated for Gus WisemanNumber of pairwise coprime sets of divisors of n, where a singleton is not considered coprime unless it is {1}.

1, 2, 2, 3, 2, 6, 2, 4, 3, 6, 2, 10, 2, 6, 6, 5, 2, 10, 2, 10, 6, 6, 2, 14, 3, 6, 4, 10, 2, 22, 2, 6, 6, 6, 6, 17, 2, 6, 6, 14, 2, 22, 2, 10, 10, 6, 2, 18, 3, 10, 6, 10, 2, 14, 6, 14, 6, 6, 2, 38, 2, 6, 10, 7, 6, 22, 2, 10, 6, 22, 2, 24, 2, 6, 10, 10, 6, 22, 2

1,2

First differs from A015995 at a(210) = 88, A015995(210) = 86.

For example, the a(n) subsets for n = 1, 2, 4, 6, 8, 12, 16, 24 are:

{1} {1} {1} {1} {1} {1} {1} {1}

{1,2} {1,2} {1,2} {1,2} {1,2} {1,2} {1,2}

{1,4} {1,3} {1,4} {1,3} {1,4} {1,3}

{1,6} {1,8} {1,4} {1,8} {1,4}

{2,3} {1,6} {1,16} {1,6}

{1,2,3} {2,3} {1,8}

{3,4} {2,3}

{1,12} {3,4}

{1,2,3} {3,8}

{1,3,4} {1,12}

{1,24}

{1,2,3}

{1,3,4}

{1,3,8}

Table[Length[Select[Subsets[Divisors[n]], CoprimeQ@@#&]], {n, 100}]

The case of pairs is A063647.

The case of triples is A066620.

The version with empty sets and singletons is A225520.

The version for prime indices is A304711.

The version for strict integer partitions is A305713.

The version for subsets of {1..n} is A320426 = A276187 + 1.

The version for binary indices is A326675.

The version for integer partitions is A327516.

The version for standard compositions is A333227.

The maximal case is A343652.

The case without 1's is A343653.

The case without 1's with singletons is A343654.

The maximal case without 1's is A343660.

A018892 counts coprime pairs of divisors.

A051026 counts pairwise indivisible subsets of {1..n}.

A100565 counts pairwise coprime triples of divisors.

A325683 counts maximal Golomb rulers.

A326077 counts maximal pairwise indivisible sets.

Cf. A000005, A076078, A282935, `A285572, `A324837, ~A326674.

Cf. A067824, A074206.

Cf. `A007360, A084422, A089233, A187106, A304709, ~A307719, A320423, ~A337462, A337485, `A337984, A343659.

Cf. ~A326496.

Cf. `A062319.

allocated

nonn

Gus Wiseman, Apr 26 2021

approved

editing

allocated for Gus Wiseman

allocated

approved