A002584 Largest prime factor of product of first n primes - 1, or 1 if no such prime exists.
1, 5, 29, 19, 2309, 30029, 8369, 929, 46027, 81894851, 876817, 38669, 304250263527209, 92608862041, 59799107, 1143707681, 69664915493, 1146665184811, 17975352936245519, 2140320249725509
Offset: 1
References
- 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).
Links
- 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.
Programs
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Mathematica
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 *) -
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
Formula
Extensions
More terms from J. L. Selfridge
Further terms from Labos Elemer, Oct 25 2000
Comments