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A057872
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A version of the Chebyshev function theta(n): a(n) = round(Sum_{primes p <= n } log(p)).
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6
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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
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OFFSET
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0,4
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COMMENTS
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See A035158, which is the main entry for this function.
The old entry with this sequence number was a duplicate of A053632.
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REFERENCES
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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.
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LINKS
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FORMULA
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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