A217254 - OEIS

%I #40 Jun 19 2021 08:39:06

%S 0,2,3,4,7,7,10,10,10,12,14,15,19,18,19,20,24,24,28,28,28,29,32,33,35,

%T 35,34,34,38,38,45,45,46,45,47,46,51,51,51,52,57,56,62,61,61,61,67,70,

%U 69,69,69,69,73,74,75,75,76,75,80,80,84,85,88,87,87,86,94

%N a(n) = round(primepi(n) * prime(n)/n).

%C For n < 10^7, a(n-1) > a(n) happens only for n composite. For n < 10^8, a(n-1) - a(n) <= 2. On the contrary, a(n) - a(n-1) seems to grow slowly and up to 10^5, 10^6, 10^7 and 10^8 is equal to 21, 26, 30, and 34, respectively. - _Giovanni Resta_, Mar 21 2013

%H Ivan Neretin, <a href="/A217254/b217254.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) ~ n. More specifically, a(n) = n + n log log n/log n + 2n log log n/log^2 n + O(n/log^2 n); the O-constant is between -1/2 and -3/2 for large n. - _Charles R Greathouse IV_, Mar 19 2013

%t Table[Floor[PrimePi[n]*Prime[n]/n + 1/2], {n, 100}] (* _T. D. Noe_, Mar 20 2013 *)

%o (PARI) a(n)=prime(n)*primepi(n)\/n \\ _Charles R Greathouse IV_, Mar 19 2013

%Y Cf. A128930.

%K nonn,less,easy

%O 1,2

%A _Alexander R. Povolotsky_, Mar 16 2013