A049084 - OEIS

%I #50 Mar 26 2024 05:40:37

%S 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,

%T 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,

%U 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

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

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

%C Equals row sums of triangle A143541. - _Gary W. Adamson_, Aug 23 2008

%H Reinhard Zumkeller, <a href="/A049084/b049084.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = pi(n)*(pi(n) - pi(n-1)), pi = A000720. - _Reinhard Zumkeller_, Nov 30 2003

%F a(n) = A000720(n*A010051(n)). - _Labos Elemer_, Jan 09 2004

%F a(n) = A000720(n)*A010051(n). - _R. J. Mathar_, Mar 01 2011

%p A049084 := proc(n)

%p     local i;

%p     if isprime(n) then

%p         for i from 1 do

%p             if ithprime(i) = n then

%p                 return i;

%p             end if;

%p         end do;

%p     else

%p         return 0 ;

%p     fi;

%p end proc:

%p seq(A049084(n),n=1..120) ;

%t Table[PrimePi[n] * Boole[PrimeQ[n]], {n, 92}] (* _Jean-François Alcover_, Nov 07 2011, after _R. J. Mathar_ *)

%t Table[If[PrimeQ[n],PrimePi[n],0],{n,100}] (* _Harvey P. Dale_, Jan 09 2022 *)

%o (Haskell)

%o import Data.List (unfoldr)

%o a049084 n = a049084_list !! (fromInteger n - 1)

%o a049084_list = unfoldr x (1, 1, a000040_list) where

%o    x (i, z, ps'@(p:ps)) | i == p = Just (z, (i + 1, z + 1, ps))

%o                         | i /= p = Just (0, (i + 1, z, ps'))

%o -- _Reinhard Zumkeller_, Apr 17 2012, Mar 31 2012, Sep 15 2011

%o (PARI) a(n)=if(isprime(n),primepi(n),0) \\ _Charles R Greathouse IV_, Jan 08 2013

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

%Y Cf. A143541.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

%E Name clarified by _Alonso del Arte_, Feb 07 2020 at the suggestion of _David A. Corneth_