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

%I A319187 #75 Oct 19 2024 15:57:32
%S A319187 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,
%T A319187 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,60,60,60,60,60,60,
%U A319187 60,60,60,60,60,60,60,60,60,72,72,72,72,72,72,72,72
%N A319187 Number of pairwise coprime subsets of {1,...,n} of maximum cardinality (A036234).
%C A319187 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.
%H A319187 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Decembre-2020-4e-defi.html">Décembre 2020, 4e défi</a> (in French), Images des Mathématiques, CNRS, 2020.
%F A319187 a(n) = Product_{p prime <= n} floor(log_p(n)).
%F A319187 a(n) = A000005(A045948(n)). - _Ridouane Oudra_, Sep 02 2019
%e A319187 The a(8) = 3 subsets are {1,2,3,5,7}, {1,3,4,5,7}, {1,3,5,7,8}.
%t A319187 Table[Length[Select[Subsets[Range[n],{PrimePi[n]+1}],CoprimeQ@@#&]],{n,24}] (* see A186974 for a faster program *)
%o A319187 (PARI) a(n) = prod(p=1, n, if (isprime(p), logint(n, p), 1)); \\ _Michel Marcus_, Dec 26 2020
%Y A319187 Rightmost terms of A186974 and A320436.
%Y A319187 Run lengths are A053707.
%Y A319187 Cf. A015614, A036234, A051424, A085945, A186971, A186972, A186994, A276187, A303139, A320423, A320426.
%Y A319187 Cf. A000005, A045948.
%K A319187 nonn
%O A319187 1,4
%A A319187 _Gus Wiseman_, Jan 09 2019