Search: id:A034387
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%I A034387
%S A034387 0,2,5,5,10,10,17,17,17,17,28,28,41,41,41,41,58,58,77,77,77,77,
%T A034387 100,100,100,100,100,100,129,129,160,160,160,160,160,160,197,197,197,
%U A034387 197,238,238,281,281,281,281,328,328,328,328,328,328
%N A034387 Sum of primes <= n.
%C A034387 Also sum of all prime-factors in n!.
%C A034387 For large n, these numbers can be closely approximated by the number 
               of primes < n^2. For example, the sum of primes < 10^10 = 2220822432581729238. 
               The number of primes < (10^10)^2 or 10^20 = 2220819602560918840. 
               This has a relative error of 0.0000012743... - Cino Hilliard (hillcino368(AT)hotmail.com), 
               Jun 08 2008
%C A034387 Equals row sums of triangle A143537 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Aug 23 2008]
%C A034387 a(n) = A158662(n) - 1. a(p) - a(p-1) = p, for p = primes (A000040), a(c) 
               - a(c-1) = 0, for c = composite numbers (A002808). [From Jaroslav 
               Krizek (jaroslav.krizek(AT)atlas.cz), Mar 23 2009]
%H A034387 T. D. Noe, <a href="b034387.txt">Table of n, a(n) for n=1..10000</a>
%H A034387 Cino Hilliard, <a href="http://docs.google.com/Doc?docid=dgpq9w4b_26dtrq634m&hl=en"> 
               Sum of primes </a>
%F A034387 From the prime number theorem a(n) has the asymptotic expression: a(n) 
               ~ n^2 / (2 log n) - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), 
               Apr 07 2001
%t A034387 s=0;lst={};Do[If[PrimeQ[n],s+=n];AppendTo[lst,s],{n,5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jun 13 2009]
%o A034387 (PARI) a(n)=sum(i=1,primepi(n),prime(i)) [From Michael Porter (michael_b_porter(AT)yahoo.com), 
               Sep 22 2009]
%Y A034387 Cf. A007504.
%Y A034387 A143537 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 23 2008]
%Y A034387 Cf. A158662, A000040, A002808. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Mar 23 2009]
%Y A034387 Sequence in context: A070243 A050175 A059797 this_sequence A081240 A132295 
               A086651
%Y A034387 Adjacent sequences: A034384 A034385 A034386 this_sequence A034388 A034389 
               A034390
%K A034387 nonn,easy
%O A034387 1,2
%A A034387 N. J. A. Sloane (njas(AT)research.att.com).

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