Search: id:A038107
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%I A038107
%S A038107 0,0,2,4,6,9,11,15,18,22,25,30,34,39,44,48,54,61,66,72,78,85,92,99,105,
%T A038107 114,122,129,137,146,154,162,172,181,191,200,210,219,228,240,251,263,
%U A038107 274,283,295,306,319,329,342,357,367,378,393,409,421,434,445,457,474
%N A038107 Number of primes < n^2.
%C A038107 Also number of primes <= n^2 since n^2 is not prime.
%C A038107 Also the number of primes contained within an n X n square spiral. - 
               William A. Tedeschi (fynmun(AT)hotmail.com), Mar 03 2008
%C A038107 For large n, these numbers closely approximate the sum of primes less 
               than n. For example, n = 10^10, sum of primes < n = 2220822432581729238. 
               The number of primes < (10^10)^2 = 10^20 = 2220819602560918840. The 
               error is 0.0000012743... The derivation of this is in the link Sum 
               of Primes. - Cino Hilliard (Hillcino368(AT)hotmail.com), Jun 09 2008
%H A038107 T. D. Noe, <a href="b038107.txt">Table of n, a(n) for n=0..1000</a>
%H A038107 Cino Hilliard, <a href="http://docs.google.com/Doc?id=dgpq9w4b_26dtrq634m">
               Sum of Primes</a>.
%e A038107 a(2)=2 because the only primes < 4 are 2 and 3.
%p A038107 A038107 := proc(n) numtheory[pi]( n^2) ; end: seq(A038107(n),n=0..100) 
               ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 22 2009]
%t A038107 Table[PrimePi[n^2], {n, 0, 100}] (*Chandler*)
%o A038107 (Other) sage: [prime_pi(n^2) for n in xrange(0, 59)] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]
%Y A038107 Cf. A014085.
%Y A038107 Sequence in context: A022760 A164286 A054519 this_sequence A153196 A077220 
               A128716
%Y A038107 Adjacent sequences: A038104 A038105 A038106 this_sequence A038108 A038109 
               A038110
%K A038107 nonn
%O A038107 0,3
%A A038107 Joe K. Crump (joecr(AT)carolina.rr.com)
%E A038107 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 22 2005

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