A057713 Smallest prime divisor of Kummer numbers ( = primorials - 1), or 1 if no such prime exists.

1, 5, 29, 11, 2309, 30029, 61, 53, 37, 79, 228737, 229, 304250263527209, 141269, 191, 87337, 27600124633, 1193, 163, 260681003321, 313, 163, 139, 23768741896345550770650537601358309, 66683, 2990092035859, 15649, 17515703, 719, 295201, 15098753, 10172884549, 20962699238647, 4871, 673, 311, 1409, 1291, 331, 1450184819, 23497, 711427, 521, 673, 519577, 1372062943, 56543, 811, 182309, 53077, 641, 349, 389

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..99

M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]

R. 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], 2012-2018. - N. J. A. Sloane, Jun 13 2012

Hisanori Mishima, Factorizations of many number sequences

R. G. Wilson v, Explicit factorizations

Formula

a(n) = A020639(A057588(n)). - Amiram Eldar, Feb 13 2020

Example

6th term in the sequence corresponds to 7th primorial = 510510 and 510509 = 61 * 8369, so a(7) = 61.

Mathematica

Map[If[PrimeQ@ #, #, FactorInteger[#][[1, 1]]] &, FoldList[#1 #2 &, Prime@ Range@ 36] - 1] (* Michael De Vlieger, Feb 18 2017 *)

Crossrefs

Cf. A002110, A002584, A002585, A006862, A020639, A057588.

Sequence in context: A033503 A181616 A057206 * A124987 A002584 A001990

Adjacent sequences: A057710 A057711 A057712 * A057714 A057715 A057716

Keyword

nonn

Author

Labos Elemer, Oct 25 2000

Extensions

More terms from Klaus Brockhaus, Larry Reeves (larryr(AT)acm.org) and Robert G. Wilson v, Apr 02 2001

Status

approved