OFFSET
1,5
COMMENTS
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).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = Product_{p in Primes with p<n and GCD(n,p)=1} floor(log_p(n)).
EXAMPLE
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}.
a(9) = 3, the maximal subsets are {1,2,5,7,9}, {1,4,5,7,9}, {1,5,7,8,9}.
MAPLE
with(numtheory):
a:= n-> mul(ilog[j](n), j={ithprime(i)$i=1..pi(n)} minus factorset(n)):
seq(a(n), n=1..200);
MATHEMATICA
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 *)
CROSSREFS
AUTHOR
Alois P. Heinz, Mar 01 2011
STATUS
approved