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 A057872 A version of the Chebyshev function theta(n): a(n) = round(Sum_{primes p <= n } log(p)). 6
 0, 0, 1, 2, 2, 3, 3, 5, 5, 5, 5, 8, 8, 10, 10, 10, 10, 13, 13, 16, 16, 16, 16, 19, 19, 19, 19, 19, 19, 23, 23, 26, 26, 26, 26, 26, 26, 30, 30, 30, 30, 33, 33, 37, 37, 37, 37, 41, 41, 41, 41, 41, 41, 45, 45, 45, 45, 45, 45, 49, 49, 53, 53, 53, 53, 53, 53, 57, 57, 57, 57, 62, 62, 66, 66, 66, 66 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See A035158, which is the main entry for this function. The old entry with this sequence number was a duplicate of A053632. REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 340. D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.35, p. 267. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 FORMULA theta(n) = log(A034386(n)). a(n) ~ n, a statement equivalent to the Prime Number Theorem. - Charles R Greathouse IV, Sep 23 2012 PROG (PARI) v=List(); t=0; for(n=0, 100, if(isprime(n), t+=log(n)); listput(v, round(t))); Vec(v) \\ Charles R Greathouse IV, Sep 23 2012 CROSSREFS Cf. A034386, A215259, A215260. Sequence in context: A259788 A033302 A072729 * A059974 A045767 A108221 Adjacent sequences:  A057869 A057870 A057871 * A057873 A057874 A057875 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 02 2008 STATUS approved

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Last modified January 16 06:59 EST 2019. Contains 319188 sequences. (Running on oeis4.)