

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
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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



