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%I #12 May 13 2013 01:54:05
%S 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,
%T 19,19,23,23,26,26,26,26,26,26,30,30,30,30,33,33,37,37,37,37,41,41,41,
%U 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
%N A version of the Chebyshev function theta(n): a(n) = round(Sum_{primes p <= n } log(p)).
%C See A035158, which is the main entry for this function.
%C The old entry with this sequence number was a duplicate of A053632.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 340.
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.35, p. 267.
%H Charles R Greathouse IV, <a href="/A057872/b057872.txt">Table of n, a(n) for n = 0..10000</a>
%F theta(n) = log(A034386(n)).
%F a(n) ~ n, a statement equivalent to the Prime Number Theorem. - _Charles R Greathouse IV_, Sep 23 2012
%o (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
%Y Cf. A034386, A215259, A215260.
%K nonn
%O 0,4
%A _N. J. A. Sloane_, Oct 02 2008
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