A319187 - OEIS

%I #75 Oct 19 2024 15:57:32

%S 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 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,60,60,60,60,60,60,

%U 60,60,60,60,60,60,60,60,60,72,72,72,72,72,72,72,72

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

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

%F a(n) = A000005(A045948(n)). - _Ridouane Oudra_, Sep 02 2019

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

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

%o (PARI) a(n) = prod(p=1, n, if (isprime(p), logint(n, p), 1)); \\ _Michel Marcus_, Dec 26 2020

%Y Rightmost terms of A186974 and A320436.

%Y Run lengths are A053707.

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

%Y Cf. A000005, A045948.

%K nonn

%O 1,4

%A _Gus Wiseman_, Jan 09 2019