A002588 a(n) = largest noncomposite factor of 2^(2n+1) - 1.

1, 7, 31, 127, 73, 89, 8191, 151, 131071, 524287, 337, 178481, 1801, 262657, 2089, 2147483647, 599479, 122921, 616318177, 121369, 164511353, 2099863, 23311, 13264529, 4432676798593, 131071, 20394401, 201961, 1212847, 3203431780337

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) is also the largest noncomposite factor of A147590(n). - César Aguilera, Jul 31 2019

References

• J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
• M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 84.
• 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

• Max Alekseyev, Table of n, a(n) for n = 0..602 (terms 1..494 from Sean A. Irvine)
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A002184, A005420, A147590.

Programs

Magma

[1] cat [Maximum(PrimeDivisors(2^(2*n+1) - 1)): n in [1..60]]; // Vincenzo Librandi, Aug 02 2019

Mathematica

Table[FactorInteger[2^(2 n + 1) - 1] [[-1, 1]], {n, 0, 30}] (* Vincenzo Librandi, Aug 02 2019 *)

PARI

a(n) = if (n==0, 1, vecmax(factor(2^(2*n+1) - 1)[, 1])); \\ Michel Marcus, Aug 03 2019

Extensions

More terms from Don Reble, Nov 14 2006