

A007053


Number of primes <= 2^n.
(Formerly M1018)


128



0, 1, 2, 4, 6, 11, 18, 31, 54, 97, 172, 309, 564, 1028, 1900, 3512, 6542, 12251, 23000, 43390, 82025, 155611, 295947, 564163, 1077871, 2063689, 3957809, 7603553, 14630843, 28192750, 54400028, 105097565, 203280221, 393615806, 762939111, 1480206279, 2874398515, 5586502348, 10866266172, 21151907950, 41203088796, 80316571436, 156661034233, 305761713237, 597116381732, 1166746786182, 2280998753949, 4461632979717, 8731188863470, 17094432576778, 33483379603407, 65612899915304, 128625503610475
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OFFSET

0,3


COMMENTS

Conjecture: The number 4 is the only perfect power in this sequence. In other words, it is impossible to have a(n) = x^m for some integers n > 3, m > 1 and x > 1.  ZhiWei Sun, Sep 30 2015


REFERENCES

Jens Franke et al., pi(10^24), Posting to the Number Theory Mailing List, Jul 29 2010.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

David Baugh, Table of n, a(n) for n = 0..92 (terms n = 87..92 found using Kim Walisch's primecount program, terms n = 0..86 from Charles R Greathouse IV and Douglas B. Staple, [a(0)a(75) from Tomás Oliveira e Silva, a(76)a(77) from Jens Franke et al., Jul 29 2010, a(78)a(80) from Jens Franke et al. on the Riemann Hypothesis, verified unconditionally by Douglas B. Staple, and a(81)a(86) from Douglas B. Staple])


FORMULA



EXAMPLE

pi(2^3)=4 since first 4 primes are 2,3,5,7 all <= 2^3 = 8.


MATHEMATICA



PROG



CROSSREFS



KEYWORD

nonn,nice


AUTHOR



EXTENSIONS

Extended to n = 52 by Warren D. Smith, Dec 11 2000, computed with MeisselLehmerLegendre inclusion exclusion formula code he wrote back in 1985, recently rerun.


STATUS

approved



