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

%I A057713 #28 Feb 13 2020 20:14:13
%S A057713 1,5,29,11,2309,30029,61,53,37,79,228737,229,304250263527209,141269,
%T A057713 191,87337,27600124633,1193,163,260681003321,313,163,139,
%U A057713 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
%N A057713 Smallest prime divisor of Kummer numbers ( = primorials - 1), or 1 if no such prime exists.
%H A057713 Amiram Eldar, <a href="/A057713/b057713.txt">Table of n, a(n) for n = 1..99</a>
%H A057713 M. Kraitchik, <a href="/A002582/a002582.pdf">On the divisibility of factorials</a>, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
%H A057713 R. 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], 2012-2018. - _N. J. A. Sloane_, Jun 13 2012
%H A057713 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H A057713 R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>
%F A057713 a(n) = A020639(A057588(n)). - _Amiram Eldar_, Feb 13 2020
%e A057713 6th term in the sequence corresponds to 7th primorial = 510510 and 510509 = 61 * 8369, so a(7) = 61.
%t A057713 Map[If[PrimeQ@ #, #, FactorInteger[#][[1, 1]]] &, FoldList[#1 #2 &, Prime@ Range@ 36] - 1] (* _Michael De Vlieger_, Feb 18 2017 *)
%Y A057713 Cf. A002110, A002584, A002585, A006862, A020639, A057588.
%K A057713 nonn
%O A057713 1,2
%A A057713 _Labos Elemer_, Oct 25 2000
%E A057713 More terms from _Klaus Brockhaus_, Larry Reeves (larryr(AT)acm.org) and _Robert G. Wilson v_, Apr 02 2001