A002584 Largest prime factor of product of first n primes - 1, or 1 if no such prime exists. (Formerly M3952 N1628)

1, 5, 29, 19, 2309, 30029, 8369, 929, 46027, 81894851, 876817, 38669, 304250263527209, 92608862041, 59799107, 1143707681, 69664915493, 1146665184811, 17975352936245519, 2140320249725509

Offset

1,2

Comments

The products of the first primes are called primorial numbers. - Franklin T. Adams-Watters, Jun 12 2014

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.

Formula

a(n) = A006530(A057588(n)). - Amiram Eldar, Feb 13 2020

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 *)

Prog

(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

Crossrefs

Cf. A002110, A002585, A006530, A057588.

Sequence in context: A057206 A057713 A124987 * A001990 A043062 A321701

Adjacent sequences: A002581 A002582 A002583 * A002585 A002586 A002587

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from J. L. Selfridge

Further terms from Labos Elemer, Oct 25 2000

Status

approved