

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
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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



