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%I #25 Dec 09 2014 04:56:32
%S 1,1,1,1,2,1,2,1,3,2,6,1,6,2,3,2,8,1,8,2,4,2,8,1,8,4,8,6,24,1,24,6,10,
%T 6,15,2,30,6,10,3,30,2,30,6,5,6,30,2,30,6,20,12,60,4,30,6,20,12,60,2,
%U 60,12,10,12,36,4,72,12,24,3,72,4,72,12,12,12,36
%N Number of maximal subsets of {1, 2, ..., n} containing n and having pairwise coprime elements.
%C The elements of a maximal subset are 1, n, and powers of primes that have no common factor with n. The cardinalities of maximal subsets is A186971(n).
%H Alois P. Heinz, <a href="/A186994/b186994.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Product_{p in Primes with p<n and GCD(n,p)=1} floor(log_p(n)).
%e a(5) = 2 because there are 2 maximal subsets of {1,2,3,4,5} containing 5 and having pairwise coprime elements: {1,2,3,5}, {1,3,4,5}.
%e a(9) = 3, the maximal subsets are {1,2,5,7,9}, {1,4,5,7,9}, {1,5,7,8,9}.
%p with(numtheory):
%p a:= n-> mul(ilog[j](n), j={ithprime(i)$i=1..pi(n)} minus factorset(n)):
%p seq(a(n), n=1..200);
%t a[n_] := Product[Log[p, n] // Floor, {p, Select[Range[n-1], PrimeQ[#] && GCD[n, #] == 1&]}]; Table[a[n], {n, 1, 200}] (* _Jean-François Alcover_, Dec 09 2014, after _Alois P. Heinz_ *)
%Y Cf. A186971. Rightmost elements in rows of A186972.
%K nonn,look,hear
%O 1,5
%A _Alois P. Heinz_, Mar 01 2011
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