A057872 A version of the Chebyshev function theta(n): a(n) = round(Sum_{primes p <= n } log(p)).

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

Offset: 0

Author

N. J. A. Sloane, Oct 02 2008

Keywords

• nonn

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

Crossrefs

Cf. A034386, A215259, A215260.

Programs

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

Formula

theta(n) = log(A034386(n)).

a(n) ~ n, a statement equivalent to the Prime Number Theorem. - Charles R Greathouse IV, Sep 23 2012