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A319187 Number of pairwise coprime subsets of {1,...,n} of maximum cardinality (A036234). 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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 *)

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

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Last modified December 2 18:08 EST 2020. Contains 338887 sequences. (Running on oeis4.)