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%I #38 Dec 13 2021 16:14:14
%S 2,3,2,4,2,7,2,3,2,4,2,6,2,3,2,4,2,7,2,3,2,4,2,5,2,3,2,4,2,9,2,3,2,4,
%T 2,8,2,3,2,4,2,6,2,3,2,4,2,7,2,3,2,4,2,5,2,3,2,4,2,11,2,3,2,4,2,8,2,3,
%U 2,4,2,6,2,3,2,4,2,7,2,3,2,4,2,5,2,3,2
%N a(n) is the greatest k > 0 such that 1+n, 1+2*n, ..., 1+n*k are pairwise coprime.
%C This sequence is well defined: for any n > 0, if p > 1 divides 1+n, then p divides 1+n*(1+p), gcd(1+n, 1+n*(1+p)) > 1 and a(n) <= p.
%C This sequence is unbounded.
%H Antti Karttunen, <a href="/A339749/b339749.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = 2 for any odd n.
%F a(n!) > n for any n >= 0.
%F a(n) <= A020639(n+1).
%e For n = 2:
%e - gcd(1+2*1, 1+2*2) = 1,
%e - gcd(1+2*1, 1+2*3) = 1,
%e - gcd(1+2*2, 1+2*3) = 1,
%e - however gcd(1+2*1, 1+2*4) = 3,
%e - so a(2) = 3.
%o (PARI) a(n) = { my (p=1); for (k=1, oo, if (gcd(p, 1+n*k)>1, return (k-1), p*=1+n*k)) }
%Y Cf. A020639, A339743, A339759.
%K nonn
%O 1,1
%A _Rémy Sigrist_, Dec 16 2020
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