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Search: id:A035158
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| A035158 |
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A version of the Chebyshev function theta(n): a(n) = floor(Sum_{primes p <= n } log(p)). |
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3
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| 0, 0, 1, 1, 3, 3, 5, 5, 5, 5, 7, 7, 10, 10, 10, 10, 13, 13, 16, 16, 16, 16, 19, 19, 19, 19, 19, 19, 22, 22, 26, 26, 26, 26, 26, 26, 29, 29, 29, 29, 33, 33, 37, 37, 37, 37, 40, 40, 40, 40, 40, 40, 44, 44, 44, 44, 44, 44, 49, 49, 53, 53, 53, 53, 53, 53, 57, 57, 57, 57, 61, 61, 65, 65, 65, 65
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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The old entry with this sequence number was a duplicate of A002325.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, see Chap. 22.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.35. (For inequalities, etc.)
J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. Journ. Math. 6 (1962) 64-94.
J. Barkley Rosser and Lowell Schoenfeld, Sharper bounds for the Chebyshev functions theta(x) and psi(x), Math. Comp. 29 (1975), no. 129, 243-269.
Schoenfeld, Lowell, Corrigendum: "Sharper bounds for the Chebyshev functions theta(x) and psi(x). II" (Math. Comput. 30 (1976), number 134, 337-360). Math. Comp. 30 (1976), number 136, 900.
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LINKS
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J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers (scan of some key pages from an ancient annotated photocopy)
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MAPLE
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(Maple for A035158, A057872, A083535:)
Digits:=2000;
tf:=[]; tr:=[]; tc:=[];
for n from 1 to 120 do
t2:=0;
j:=pi(n);
for i from 1 to j do t2:=t2+log(ithprime(i)); od;
tf:=[op(tf), floor(evalf(t2))];
tr:=[op(tr), round(evalf(t2))];
tc:=[op(tc), ceil(evalf(t2))];
od:
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CROSSREFS
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Cf. A057872, A083535.
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KEYWORD
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nonn,new
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AUTHOR
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njas, Oct 02 2008
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