A065317 - OEIS

%I #34 Jun 17 2024 15:57:43

%S 5,11,37,17,101,30047,510529,9699713,1427,76829,789077,659863,

%T 810104837,13082761331670077,652833094897,32589158477190044789,

%U 1922760350154212639131,28406001782370300553,770555057,94904036422299534098897,40729680599249024150621323549

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

%H Tyler Busby, <a href="/A065317/b065317.txt">Table of n, a(n) for n = 1..84</a> (terms 1..68 from Daniel Suteu, terms 69..79 from Sean A. Irvine)

%H Romeo Mestrovic, <a href="http://arxiv.org/abs/1202.3670">Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof</a>, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2023. - From _N. J. A. Sloane_, Jun 13 2012

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

%F a(n) = A006530(A060881(n)). - _Michel Marcus_, Sep 08 2023

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

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

%o (PARI) a(n) = vecmax(factor(vecprod(primes(n)) + prime(n+1))[,1]); \\ _Daniel Suteu_, May 26 2022

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

%Y See also A065314, A065315, A065316.

%K nonn

%O 1,1

%A _Labos Elemer_, Oct 29 2001

%E Name clarified by _Felix Fröhlich_, May 26 2022