A065317 Largest prime divisor of the sum of the n-th primorial and the (n+1)-st prime.

5, 11, 37, 17, 101, 30047, 510529, 9699713, 1427, 76829, 789077, 659863, 810104837, 13082761331670077, 652833094897, 32589158477190044789, 1922760350154212639131, 28406001782370300553, 770555057, 94904036422299534098897, 40729680599249024150621323549

Offset: 1

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Examples

			For n = 4, 4th primorial = 210, prime(5) = 11, sum = 210 + 11 = 13 * 17, a(4) = 17.
		

Links

• Tyler Busby, Table of n, a(n) for n = 1..84 (terms 1..68 from Daniel Suteu, terms 69..79 from Sean A. Irvine)
• Romeo Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From _N. J. A. Sloane_, Jun 13 2012

Crossrefs

Cf. A002110, A000040, A060881, A006530, A057713, A002584, A002585, A051342.

See also A065314, A065315, A065316.

Programs

Mathematica

With[{nn=20},FactorInteger[#][[-1,1]]&/@(Total/@Thread[{FoldList[ Times,Prime[Range[nn]]],Prime[Range[nn]+1]}])] (* Harvey P. Dale, Jul 26 2020 *)

PARI

a(n) = vecmax(factor(vecprod(primes(n)) + prime(n+1))[,1]); \\ Daniel Suteu, May 26 2022

Formula

a(n) = A006530(A002110(n) + A000040(n+1)).

a(n) = A006530(A060881(n)). - Michel Marcus, Sep 08 2023

Extensions

Name clarified by Felix Fröhlich, May 26 2022