A002588 a(n) = largest noncomposite factor of 2^(2n+1) - 1. (Formerly M4401 N1856)

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

0,2

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

Mathematica

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

Prog

(PARI) a(n) = if (n==0, 1, vecmax(factor(2^(2*n+1) - 1)[, 1])); \\ Michel Marcus, Aug 03 2019
(Magma) [1] cat [Maximum(PrimeDivisors(2^(2*n+1) - 1)): n in [1..60]]; // Vincenzo Librandi, Aug 02 2019

Crossrefs

Cf. A002184, A005420, A147590.

Sequence in context: A218963 A125193 A002184 * A327497 A036280 A153005

Adjacent sequences: A002585 A002586 A002587 * A002589 A002590 A002591

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Don Reble, Nov 14 2006

Status

approved