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A002584 Largest prime factor of product of first n primes - 1.
(Formerly M3952 N1628)
8

%I M3952 N1628

%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.

%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, <a href="/A002584/b002584.txt">Table of n, a(n) for n = 1..91</a>

%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>.

%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. A002585, A002110.

%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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Last modified November 21 11:35 EST 2019. Contains 329370 sequences. (Running on oeis4.)