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%I M3952 N1628 #55 Feb 13 2020 11:57:10
%S 1,5,29,19,2309,30029,8369,929,46027,81894851,876817,38669,
%T 304250263527209,92608862041,59799107,1143707681,69664915493,
%U 1146665184811,17975352936245519,2140320249725509
%N Largest prime factor of product of first n primes - 1, or 1 if no such prime exists.
%C The products of the first primes are called primorial numbers. - _Franklin T. Adams-Watters_, Jun 12 2014
%D M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
%D M. Kraitchik, Introduction à la Théorie des Nombres. Gauthier-Villars, Paris, 1952, p. 2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Sean A. Irvine and Amiram Eldar, <a href="/A002584/b002584.txt">Table of n, a(n) for n = 1..99</a> (terms 1..91 from Sean A. Irvine)
%H A. Borning, <a href="http://dx.doi.org/10.1090/S0025-5718-1972-0308018-5 ">Some results for k!+-1 and 2.3.5...p+-1</a>, Math. Comp., 26 (1972), 567-570.
%H 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 S. Kravitz and D. E. Penney, <a href="http://www.jstor.org/stable/2689826">An extension of Trigg's table</a>, Math. Mag., 48 (1975), 92-96.
%H S. Kravitz and D. E. Penney, <a href="/A002584/a002584.pdf">An extension of Trigg's table</a>, Math. Mag., 48 (1975), 92-96. [Annotated scanned copy; also letter from N. J. A. Sloane to John Selfridge]
%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>
%H John Selfridge, Marvin Wunderlich, Robert Morris, N. J. A. Sloane, <a href="/A002584/a002584_1.pdf">Correspondence, 1975</a>
%H R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>.
%F a(n) = A006530(A057588(n)). - _Amiram Eldar_, Feb 13 2020
%t Prepend[Table[ Max[Transpose[FactorInteger[(Times @@ Prime[Range[i]]) - 1]][[1]]], {i, 2, 20}], 1]
%t FactorInteger[#][[-1,1]]&/@Rest[FoldList[Times,1,Prime[Range[20]]]-1] (* _Harvey P. Dale_, Feb 27 2013 *)
%o (PARI) a(n)=if(n>1, my(f=factor(prod(i=1,f,prime(i)))[,1]); f[#f], 1) \\ _Charles R Greathouse IV_, Feb 08 2017
%Y Cf. A002110, A002585, A006530, A057588.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from J. L. Selfridge
%E Further terms from _Labos Elemer_, Oct 25 2000
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