OFFSET
1,2
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
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
MATHEMATICA
Table[Floor[PrimePi[n]*Prime[n]/n + 1/2], {n, 100}] (* T. D. Noe, Mar 20 2013 *)
PROG
(PARI) a(n)=prime(n)*primepi(n)\/n \\ Charles R Greathouse IV, Mar 19 2013
CROSSREFS
KEYWORD
nonn,less,easy
AUTHOR
Alexander R. Povolotsky, Mar 16 2013
STATUS
approved