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 A186994 Number of maximal subsets of {1, 2, ..., n} containing n and having pairwise coprime elements. 6
 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, 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, 60, 12, 10, 12, 36, 4, 72, 12, 24, 3, 72, 4, 72, 12, 12, 12, 36 (list; graph; refs; listen; history; text; internal format)
 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 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 Cf. A186971. Rightmost elements in rows of A186972. Sequence in context: A269572 A029198 A029175 * A056889 A275761 A232396 Adjacent sequences: A186991 A186992 A186993 * A186995 A186996 A186997 KEYWORD nonn,look,hear AUTHOR Alois P. Heinz, Mar 01 2011 STATUS approved

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Last modified January 30 05:43 EST 2023. Contains 359939 sequences. (Running on oeis4.)