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%I #20 Feb 19 2014 02:27:14
%S 0,0,3,6,15,19,37,47,69,82,113,139,180,216,244,300,381,423,486,553,
%T 638,726,820,887,1029,1152,1256,1376,1527,1659,1794,1992,2156,2357,
%U 2517,2739,2909,3085,3365,3627,3933,4200,4380,4687,4960,5313,5547,5917,6395
%N Number of primes below n^3 does not exceed n times the number of primes below n^2.
%H Vincenzo Librandi, <a href="/A060304/b060304.txt">Table of n, a(n) for n = 0..1000</a>
%H S. Segal, <a href="http://dx.doi.org/10.1090/S0002-9947-1962-0139586-4">On π(x+y)<=π(x)+π(y)</a>, Transactions American Mathematical Society, 104 (1962), 523-527.
%F a(n) = n*pi(n*n) - pi(n*n*n). - _Jonathan Sondow_, Feb 17 2014
%F a(n) = n*A038107(n) - A038098(n). - _Michel Marcus_, Feb 17 2014
%e n=10, 10*pi(100)=250, pi(1000)=168, a(10)=250-168=82.
%t Table[n*PrimePi[n^2]-PrimePi[n^3], {n, 1, 100}]
%Y Cf. A060199, A060208, A000720.
%K nonn
%O 0,3
%A _Labos Elemer_, Mar 26 2001
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