A057872 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

See A035158, which is the main entry for this function.

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 A390842 A045767

Adjacent sequences: A057869 A057870 A057871 * A057873 A057874 A057875

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 02 2008

STATUS

approved