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A006514 Primes p such that 2^p - 1 has at most 2 prime factors.
(Formerly M0653)
0
2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 59, 61, 67, 83, 89, 97, 101, 103, 107, 109, 127, 131, 137, 139, 149, 167, 197, 199, 227, 241, 269, 271, 281, 293, 347, 373, 379, 421, 457, 487, 521, 523, 607, 727, 809, 881, 971, 983, 997, 1061, 1063 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For a composite n, number 2^n - 1 has at most 2 prime factors only if n = p^2, where p is prime from the intersection of A000043 and A156585. The only known such primes are 2, 3, 7. - Max Alekseyev, Apr 23 2019

a(54) >= 1277. - Max Alekseyev, Apr 23 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.

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

LINKS

Table of n, a(n) for n=1..53.

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

Select[Prime[Range[100]], PrimeOmega[2^#-1]<3&] (* Harvey P. Dale, Nov 11 2011 *)

CROSSREFS

Cf. A000043 (a subsequence), A001348, A088863.

Sequence in context: A216881 A042966 A128898 * A216286 A086983 A303436

Adjacent sequences:  A006511 A006512 A006513 * A006515 A006516 A006517

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Sean A. Irvine, May 04 2017

Edited by Max Alekseyev, Apr 23 2019

STATUS

approved

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Last modified April 18 05:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)