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 A003260 Largest prime factor of n-th Mersenne number (A001348(n)). (Formerly M2693) 11
 3, 7, 31, 127, 89, 8191, 131071, 524287, 178481, 2089, 2147483647, 616318177, 164511353, 2099863, 13264529, 20394401, 3203431780337, 2305843009213693951 (list; graph; refs; listen; history; text; internal format)
 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 T. D. Noe and 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 STATUS approved

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Last modified August 8 05:25 EDT 2020. Contains 336290 sequences. (Running on oeis4.)