A092967 Largest prime of the form a squarefree number + 1 where the prime divisors of the squarefree number are < n.

2, 3, 7, 7, 31, 31, 211, 211, 211, 211, 2311, 2311, 6007, 6007, 6007, 6007, 102103, 102103, 3233231, 3233231, 3233231, 3233231, 17160991

Offset

1,1

Comments

Conjecture: a(n)-1 has prime(n)-1 divisors. Subsidiary sequence: Number of primes of the form 2*p*q*r*...+1 where p, q, r, etc. are distinct odd primes < n.

Links

Table of n, a(n) for n=1..23.

Example

a(13) = 6007 = 2*3*7*11*13 + 1, as 2*5*7*11*13 + 1, etc. are composite.

Mathematica

<<DiscreteMath`; <<NumberTheory`; Do[l = Select[Map[Times @@ #&, Subsets[Range[n]]], SquareFreeQ]; Print[Max[Select[Map[ #+1&, l], PrimeQ]]], {n, 1, 30}] (* Ryan Propper, Aug 13 2005 *)

Crossrefs

Cf. A092965, A060957.

Sequence in context: A104138 A281909 A083809 * A056431 A281947 A199466

Adjacent sequences: A092964 A092965 A092966 * A092968 A092969 A092970

Keyword

nonn

Author

Amarnath Murthy, Mar 26 2004

Extensions

More terms from Ryan Propper, Aug 13 2005

Status

approved