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A038107
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Number of primes < n^2.
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14
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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, 114, 122, 129, 137, 146, 154, 162, 172, 181, 191, 200, 210, 219, 228, 240, 251, 263, 274, 283, 295, 306, 319, 329, 342, 357, 367, 378, 393, 409, 421, 434, 445, 457, 474
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also number of primes <= n^2 since n^2 is not prime.
Also the number of primes contained within an n X n square spiral. - William A. Tedeschi (fynmun(AT)hotmail.com), Mar 03 2008
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
a(n) - A000720(n) = A073882(n) - A010051(n) = A117490(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Cino Hilliard, Sum of Primes.
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FORMULA
| a(n) = A000720(A000290(n)).
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EXAMPLE
| a(2)=2 because the only primes < 4 are 2 and 3.
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MAPLE
| 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]
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MATHEMATICA
| Table[PrimePi[n^2], {n, 0, 100}] (*Chandler*)
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PROG
| (Other) sage: [prime_pi(n^2) for n in xrange(0, 59)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 06 2009]
(Haskell)
a038107 n = length $ takeWhile (< a000290 n) a000040_list
-- Reinhard Zumkeller, Nov 01
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CROSSREFS
| Cf. A014085.
Cf. A111208, A194189.
Sequence in context: A164286 A054519 A168434 * A195526 A153196 A077220
Adjacent sequences: A038104 A038105 A038106 * A038108 A038109 A038110
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KEYWORD
| nonn
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AUTHOR
| Joe K. Crump (joecr(AT)carolina.rr.com)
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 22 2005
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