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A280738
After S(n)=A280864(n) has been computed, let p(n) = product of distinct primes shared by S(n-1) and S(n); let q(n) = product of distinct primes in S(n) but not in S(n-1); and let r(n) = smallest number not yet in S. Sequence gives p(n).
7
1, 1, 2, 1, 3, 2, 1, 5, 2, 3, 1, 7, 2, 1, 11, 2, 3, 5, 2, 3, 7, 2, 13, 1, 17, 2, 15, 1, 19, 2, 1, 23, 2, 3, 1, 5, 7, 6, 1, 29, 2, 5, 11, 3, 13, 2, 11, 7, 1, 31, 2, 5, 13, 6, 1, 37, 2, 7, 3, 17, 2, 15, 1, 41, 2, 1, 43, 2, 33, 1, 47, 2, 35, 3, 19, 2, 3, 23, 2, 5
OFFSET
1,3
COMMENTS
We use the convention that an empty product is 1.
By decree, gcd(S(n+1),p(n)) = 1, gcd(S(n+1),q(n)) = q(n) = p(n+1), S(n+1) >= r(n).
By definition, all terms are squarefree. Let {i,j,k} be distinct fixed positive numbers. Conjecture: All squarefree numbers appear infinitely often, and all terms a(n) = j are immediately preceded and followed infinitely often by all terms a(n-1) = i and a(n+1) = k. If so, then A280864 is a permutation of the natural numbers. - Bob Selcoe, Apr 04 2017
LINKS
CROSSREFS
Cf. A005117 (squarefree numbers).
Sequence in context: A332077 A220901 A002335 * A370628 A207375 A173302
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 12 2017
EXTENSIONS
More terms from Rémy Sigrist, Jan 14 2017
STATUS
approved