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 A007053 Number of primes <= 2^n. (Formerly M1018) 74
 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 (list; graph; refs; listen; history; text; internal format)
 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. - Zhi-Wei 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 Charles R Greathouse IV and Douglas B. Staple, Table of n, a(n) for n = 0..86 [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 RH, verified unconditionally by Douglas B. Staple, and a(81)-a(86) from Douglas B. Staple] Andrew R. Booker, The Nth Prime Page S. W. Golomb, Letter to N. J. A. Sloane, Jul. 1991 Thomas R. Nicely, Some Results of Computational Research in Prime Numbers Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x) Tomás Oliveira e Silva, Computing pi(x): the combinatorial method, Revista Do Detua, Vol. 4, No 6, March 2006. Douglas B. Staple, The combinatorial algorithm for computing pi(x), preprint, 2015. FORMULA a(n) = A060967(2n). - R. J. Mathar, Sep 15 2012 EXAMPLE pi(2^3)=4 since first 4 primes are 2,3,5,7 all <=2^3=8. MATHEMATICA Table[PrimePi[2^n], {n, 0, 46}] (* Robert G. Wilson v *) PROG (PARI) a(n) = primepi(1<

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