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A274906 Largest prime factor of 4^n - 1. 13
3, 5, 7, 17, 31, 13, 127, 257, 73, 41, 683, 241, 8191, 127, 331, 65537, 131071, 109, 524287, 61681, 5419, 2113, 2796203, 673, 4051, 8191, 262657, 15790321, 3033169, 1321, 2147483647, 6700417, 599479, 131071, 122921, 38737, 616318177, 525313, 22366891 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
FORMULA
a(n) = A006530(A024036(n)). - Michel Marcus, Jul 11 2016
a(n) = max(A002587(n),A005420(n)). - Max Alekseyev, Apr 25 2022
EXAMPLE
4^7 - 1 = 16383 = 3*43*127, so a(7) = 127
MATHEMATICA
Table[FactorInteger[4^n - 1][[-1, 1]], {n, 40}]
PROG
(Magma) [Maximum(PrimeDivisors(4^n-1)): n in [1..40]];
CROSSREFS
Second bisection of A005420. - Michel Marcus, Jul 13 2016
Cf. largest prime factor of k^n-1: A005420 (k=2), A074477 (k=3), this sequence (k=4), A074479 (k=5), A274907 (k=6), A074249 (k=7), A274908 (k=8), A274909 (k=9), A005422 (k=10), A274910 (k=11).
Sequence in context: A257592 A032496 A002092 * A296422 A174394 A057476
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Jul 11 2016
EXTENSIONS
Terms to a(100) in b-file from Vincenzo Librandi, Jul 13 2016
a(101)-a(603) in b-file from Amiram Eldar, Feb 08 2020
a(604)-a(1122) in b-file from Max Alekseyev, Jul 25 2023
STATUS
approved

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Last modified December 6 08:34 EST 2023. Contains 367600 sequences. (Running on oeis4.)