This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291538 #15 Sep 10 2017 16:39:34
%S A291538 0,3,1,10,3,20,4,33,65,104,92,144,111,184,260,348,313,422,370,495,635,
%T A291538 786,728,904,1092,1291,1498,1731,1707,1961,1897,2181,2486,2806,3152,
%U A291538 3490,3466,3851,4267,4685,4653,5111,5045,5549,6066,6617,6541,7124,7723,8359,9007,9685,9650,10383,11106,11859,12669,13487,13498,14374
%N A291538 a(n) = PrimePi(n^3) - PrimePi(n)^3, where PrimePi = A000720.
%C A291538 All terms are positive except a(1) = 0, by the PNT with error term for large n and computation for smaller n. In particular, PrimePi(n^3) > PrimePi(n)^3 for n > 1. Indeed, by A291539 and A291540, PrimePi(n^3) > PrimePi(n) * PrimePi(n^2) > PrimePi(n)^3 for n > 7.
%C A291538 For prime(n)^3 - prime(n^3), see A262199.
%C A291538 For PrimePi(n^2) - PrimePi(n)^2, see A291440.
%F A291538 a(n) = A000720(n^3) - A000720(n)^3.
%F A291538 a(n) = A291539(n) + A291540(n).
%F A291538 a(n) ~ (n^3 / log(n))*(1/3 - 1/log(n)^2) as n tends to infinity.
%e A291538 a(3) = PrimePi(3^3) - PrimePi(3)^3 = 9 - 2^3 = 1.
%t A291538 Table[ PrimePi[n^3] - PrimePi[n]^3, {n, 60}]
%o A291538 (PARI) a(n) = primepi(n^3) - primepi(n)^3; \\ _Michel Marcus_, Sep 10 2017
%Y A291538 Cf. A000720, A123914, A262199, A291440, A291539, A291540, A291541, A291542.
%K A291538 nonn
%O A291538 1,2
%A A291538 _Jonathan Sondow_, following a suggestion from _Altug Alkan_, Aug 25 2017