A319187 Number of pairwise coprime subsets of {1,...,n} of maximum cardinality (A036234).

1, 1, 1, 2, 2, 2, 2, 3, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 24, 24, 24, 24, 24, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 72, 72, 72, 72, 72, 72, 72, 72

Offset

1,4

Comments

Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1. A single number is not considered to be pairwise coprime unless it is equal to 1.

Links

Table of n, a(n) for n=1..71.

Ana Rechtman, Décembre 2020, 4e défi (in French), Images des Mathématiques, CNRS, 2020.

Formula

a(n) = Product_{p prime <= n} floor(log_p(n)).

a(n) = A000005(A045948(n)). - Ridouane Oudra, Sep 02 2019

Example

The a(8) = 3 subsets are {1,2,3,5,7}, {1,3,4,5,7}, {1,3,5,7,8}.

Mathematica

Table[Length[Select[Subsets[Range[n], {PrimePi[n]+1}], CoprimeQ@@#&]], {n, 24}] (* see A186974 for a faster program *)

Prog

(PARI) a(n) = prod(p=1, n, if (isprime(p), logint(n, p), 1)); \\ Michel Marcus, Dec 26 2020

Crossrefs

Rightmost terms of A186974 and A320436.

Run lengths are A053707.

Cf. A015614, A036234, A051424, A085945, A186971, A186972, A186994, A276187, A303139, A320423, A320426.

Cf. A000005, A045948.

Sequence in context: A225941 A138705 A333528 * A248780 A213021 A078228

Adjacent sequences: A319184 A319185 A319186 * A319188 A319189 A319190

Keyword

nonn

Author

Gus Wiseman, Jan 09 2019

Status

approved