%I #13 Mar 25 2014 10:17:04

%S 1,2,2,2,3,3,3,4,4,4,4,5,5,5,6,6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,

%T 10,11,11,11,11,11,12,12,12,12,13,13,13,13,13,14,14,14,14,15,15,15,15,

%U 15,16,16,16,16,16,17,17,17,17,18,18,18,18,18,19,19

%N Integer nearest to (Li(n) - Li(sqrt(n))), where Li(x) = integral(0..x, dt/log(t)).

%C Challenge: find the smallest n for which pi(n) < a(n), where pi(n) is the prime counting function.

%H Arkadiusz Wesolowski, <a href="/A222642/b222642.txt">Table of n, a(n) for n = 2..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">Prime number theorem</a>

%t Table[Round[LogIntegral[n] - LogIntegral@Sqrt[n]], {n, 2, 74}]

%o (PARI) a(n)=round(real(eint1(-log(n)/2)-eint1(-log(n)))) \\ _Charles R Greathouse IV_, Feb 27 2013

%Y Cf. A047743.

%K nonn

%O 2,2

%A _Arkadiusz Wesolowski_, Feb 27 2013