A217254 a(n) = round(primepi(n) * prime(n)/n).

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, 35, 34, 34, 38, 38, 45, 45, 46, 45, 47, 46, 51, 51, 51, 52, 57, 56, 62, 61, 61, 61, 67, 70, 69, 69, 69, 69, 73, 74, 75, 75, 76, 75, 80, 80, 84, 85, 88, 87, 87, 86, 94

Offset: 1

Author

Alexander R. Povolotsky, Mar 16 2013

Keywords

• nonn
• less
• easy

Comments

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

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A128930.

Programs

Mathematica

Table[Floor[PrimePi[n]*Prime[n]/n + 1/2], {n, 100}] (* T. D. Noe, Mar 20 2013 *)

PARI

a(n)=prime(n)*primepi(n)\/n \\ Charles R Greathouse IV, Mar 19 2013

Formula

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