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).

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

Author

N. J. A. Sloane, Jan 12 2017

Keywords

• nonn

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

• Rémy Sigrist, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A280864, A280740, A280741, A280742, A280743, A280744.

Cf. A005117 (squarefree numbers).

Extensions

More terms from Rémy Sigrist, Jan 14 2017