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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

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

Cf. A143541.

Programs

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

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 *)

PARI

a(n)=if(isprime(n),primepi(n),0) \\ Charles R Greathouse IV, Jan 08 2013

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

Extensions

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