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A339749
a(n) is the greatest k > 0 such that 1+n, 1+2*n, ..., 1+n*k are pairwise coprime.
3
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, 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, 2, 4, 2, 6, 2, 3, 2, 4, 2, 7, 2, 3, 2, 4, 2, 5, 2, 3, 2
OFFSET
1,1
COMMENTS
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.
This sequence is unbounded.
LINKS
FORMULA
a(n) = 2 for any odd n.
a(n!) > n for any n >= 0.
a(n) <= A020639(n+1).
EXAMPLE
For n = 2:
- gcd(1+2*1, 1+2*2) = 1,
- gcd(1+2*1, 1+2*3) = 1,
- gcd(1+2*2, 1+2*3) = 1,
- however gcd(1+2*1, 1+2*4) = 3,
- so a(2) = 3.
PROG
(PARI) a(n) = { my (p=1); for (k=1, oo, if (gcd(p, 1+n*k)>1, return (k-1), p*=1+n*k)) }
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 16 2020
STATUS
approved