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A002584
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Largest prime factor of product of first n primes - 1, or 1 if no such prime exists.
(Formerly M3952 N1628)
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8
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1, 5, 29, 19, 2309, 30029, 8369, 929, 46027, 81894851, 876817, 38669, 304250263527209, 92608862041, 59799107, 1143707681, 69664915493, 1146665184811, 17975352936245519, 2140320249725509
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OFFSET
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1,2
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COMMENTS
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The products of the first primes are called primorial numbers. - Franklin T. Adams-Watters, Jun 12 2014
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REFERENCES
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M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors).
M. Kraitchik, Introduction à la Théorie des Nombres. Gauthier-Villars, Paris, 1952, p. 2.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Sean A. Irvine and Amiram Eldar, Table of n, a(n) for n = 1..99 (terms 1..91 from Sean A. Irvine)
A. Borning, Some results for k!+-1 and 2.3.5...p+-1, Math. Comp., 26 (1972), 567-570.
M. Kraitchik, On the divisibility of factorials, Scripta Math., 14 (1948), 24-26 (but beware errors). [Annotated scanned copy]
S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96.
S. Kravitz and D. E. Penney, An extension of Trigg's table, Math. Mag., 48 (1975), 92-96. [Annotated scanned copy; also letter from N. J. A. Sloane to John Selfridge]
Hisanori Mishima, Factorizations of many number sequences
John Selfridge, Marvin Wunderlich, Robert Morris, N. J. A. Sloane, Correspondence, 1975
R. G. Wilson v, Explicit factorizations.
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FORMULA
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a(n) = A006530(A057588(n)). - Amiram Eldar, Feb 13 2020
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MATHEMATICA
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Prepend[Table[ Max[Transpose[FactorInteger[(Times @@ Prime[Range[i]]) - 1]][[1]]], {i, 2, 20}], 1]
FactorInteger[#][[-1, 1]]&/@Rest[FoldList[Times, 1, Prime[Range[20]]]-1] (* Harvey P. Dale, Feb 27 2013 *)
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PROG
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(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
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CROSSREFS
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Cf. A002110, A002585, A006530, A057588.
Sequence in context: A057206 A057713 A124987 * A001990 A043062 A321701
Adjacent sequences: A002581 A002582 A002583 * A002585 A002586 A002587
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from J. L. Selfridge
Further terms from Labos Elemer, Oct 25 2000
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STATUS
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approved
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