A280738 - OEIS

%I #33 Apr 05 2017 07:59:44

%S 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,

%T 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,

%U 15,1,41,2,1,43,2,33,1,47,2,35,3,19,2,3,23,2,5

%N 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).

%C We use the convention that an empty product is 1.

%C 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).

%C 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

%H Rémy Sigrist, <a href="/A280738/b280738.txt">Table of n, a(n) for n = 1..100000</a>

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

%Y Cf. A005117 (squarefree numbers).

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jan 12 2017

%E More terms from _Rémy Sigrist_, Jan 14 2017