A003260 Largest prime factor of n-th Mersenne number (A001348(n)). (Formerly M2693)

3, 7, 31, 127, 89, 8191, 131071, 524287, 178481, 2089, 2147483647, 616318177, 164511353, 2099863, 13264529, 20394401, 3203431780337, 2305843009213693951

Offset

1,1

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Michel Marcus and Gord Palameta, Table of n, a(n) for n = 1..197 (first 95 terms from T. D. Noe, derived from Brillhart et al.)

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

C. K. Caldwell, Mersenne primes

P. Erdős and T. N. Shorey, On the greatest prime factor of 2^p—1 for a prime p and other expressions, Acta Arith. 30:3 (1976), pp. 257-265.

C. L. Stewart, The greatest prime factor of a^n - b^n, Acta Arith. 26 (1975), pp. 427-433.

S. S. Wagstaff, Jr., The Cunningham Project

Formula

Let p = prime(n). Erdős & Shorey show that a(n) >= kp log p for some effectively computable k >= 1. (Presumably k can be chosen as 7/log 27.) - Charles R Greathouse IV, Dec 05 2012

Mathematica

a[n_] := FactorInteger[ 2^Prime[n] - 1 ][[-1, 1]]; Table[ a[n], {n, 1, 18}] (* Jean-François Alcover, Dec 20 2011 *)

Prog

(PARI) a(n)=my(f=factor(2^prime(n)-1)[, 1]); f[#f] \\ Charles R Greathouse IV, Dec 05 2012

Crossrefs

Cf. A000668 (a subsequence), A001348, A016047, A046800.

Sequence in context: A103901 A089162 A016047 * A152058 A138865 A051281

Adjacent sequences: A003257 A003258 A003259 * A003261 A003262 A003263

Keyword

nonn,nice

Author

N. J. A. Sloane

Status

approved