A049084 a(n) = pi(n) if n is prime, otherwise 0.

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

Offset

1,3

Comments

pi(n) is the prime counting function, A000720.

Equals row sums of triangle A143541. - Gary W. Adamson, Aug 23 2008

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

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

Maple

A049084 := proc(n)
    local i;
    if isprime(n) then
        for i from 1 do
            if ithprime(i) = n then
                return i;
            end if;
        end do;
    else
        return 0 ;
    fi;
end proc:
seq(A049084(n), n=1..120) ;

Mathematica

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 *)

Prog

(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

Crossrefs

a(n) = A091227(A091202(n)).

Cf. A143541.

Sequence in context: A343488 A343270 A137303 * A234580 A352740 A108416

Adjacent sequences: A049081 A049082 A049083 * A049085 A049086 A049087

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Name clarified by Alonso del Arte, Feb 07 2020 at the suggestion of David A. Corneth

Status

approved