Search: id:A035158
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%I A035158
%S A035158 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,
%T A035158 22,22,26,26,26,26,26,26,29,29,29,29,33,33,37,37,37,37,40,40,40,40,40,
               40,
%U A035158 44,44,44,44,44,44,49,49,53,53,53,53,53,53,57,57,57,57,61,61,65,65,65,
               65
%N A035158 A version of the Chebyshev function theta(n): a(n) = floor(Sum_{primes 
               p <= n } log(p)).
%C A035158 The old entry with this sequence number was a duplicate of A002325.
%D A035158 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, see Chap. 22.
%D A035158 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.35. 
               (For inequalities, etc.)
%D A035158 J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some 
               functions of prime numbers, Ill. Journ. Math. 6 (1962) 64-94.
%D A035158 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.
%D A035158 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.
%H A035158 J. Barkley Rosser and Lowell Schoenfeld, <a href="a000720.html">Approximate 
               formulas for some functions of prime numbers</a> (scan of some key 
               pages from an ancient annotated photocopy)
%p A035158 (Maple for A035158, A057872, A083535:)
%p A035158 Digits:=2000;
%p A035158 tf:=[]; tr:=[]; tc:=[];
%p A035158 for n from 1 to 120 do
%p A035158 t2:=0;
%p A035158 j:=pi(n);
%p A035158 for i from 1 to j do t2:=t2+log(ithprime(i)); od;
%p A035158 tf:=[op(tf),floor(evalf(t2))];
%p A035158 tr:=[op(tr),round(evalf(t2))];
%p A035158 tc:=[op(tc),ceil(evalf(t2))];
%p A035158 od:
%Y A035158 Cf. A057872, A083535.
%Y A035158 Sequence in context: A133772 A129972 A130829 this_sequence A123313 A131507 
               A075260
%Y A035158 Adjacent sequences: A035155 A035156 A035157 this_sequence A035159 A035160 
               A035161
%K A035158 nonn
%O A035158 1,5
%A A035158 N. J. A. Sloane (njas(AT)research.att.com), Oct 02 2008

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