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A049084
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a(n) = pi(n) if n is prime, otherwise 0.
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266
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0, 1, 2, 0, 3, 0, 4, 0, 0, 0, 5, 0, 6, 0, 0, 0, 7, 0, 8, 0, 0, 0, 9, 0, 0, 0, 0, 0, 10, 0, 11, 0, 0, 0, 0, 0, 12, 0, 0, 0, 13, 0, 14, 0, 0, 0, 15, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 17, 0, 18, 0, 0, 0, 0, 0, 19, 0, 0, 0, 20, 0, 21, 0, 0, 0, 0, 0, 22, 0, 0, 0, 23, 0, 0, 0, 0, 0, 24, 0, 0, 0
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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pi(n) is the prime counting function, A000720.
Equals row sums of triangle A143541. - Gary W. Adamson, Aug 23 2008
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = pi(n)*(pi(n) - pi(n-1)), pi = A000720. - Reinhard Zumkeller, Nov 30 2003
a(n) = A000720(n*A010051(n)). - Labos Elemer, Jan 09 2004
a(n) = A000720(n)*A010051(n). - R. J. Mathar, Mar 01 2011
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MAPLE
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A049084 := proc(n) local i; if(isprime(n)) then for i from 1 to 1000000 do if(ithprime(i) = n) then RETURN(i); fi; od; else RETURN(0); fi; end;
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MATHEMATICA
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Table[PrimePi[n] * Boole[PrimeQ[n]], {n, 92}] (* Jean-François Alcover, Nov 07 2011, after R. J. Mathar *)
Table[If[PrimeQ[n], PrimePi[n], 0], {n, 100}] (* Harvey P. Dale, Jan 09 2022 *)
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PROG
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(Haskell)
import Data.List (unfoldr)
a049084 n = a049084_list !! (fromInteger n - 1)
a049084_list = unfoldr x (1, 1, a000040_list) where
x (i, z, ps'@(p:ps)) | i == p = Just (z, (i + 1, z + 1, ps))
| i /= p = Just (0, (i + 1, z, ps'))
-- Reinhard Zumkeller, Apr 17 2012, Mar 31 2012, Sep 15 2011
(PARI) a(n)=if(isprime(n), primepi(n), 0) \\ Charles R Greathouse IV, Jan 08 2013
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CROSSREFS
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a(n) = A091227(A091202(n)).
Cf. A143541.
Sequence in context: A343488 A343270 A137303 * A234580 A352740 A108416
Adjacent sequences: A049081 A049082 A049083 * A049085 A049086 A049087
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Name clarified by Alonso del Arte, Feb 07 2020 at the suggestion of David A. Corneth
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STATUS
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approved
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