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 A291540 #12 Sep 10 2017 17:14:32
%S A291540 0,1,0,4,0,6,-4,8,24,36,25,45,18,48,72,108,84,119,64,112,168,224,162,
%T A291540 216,297,369,432,504,460,540,451,561,660,770,869,979,900,1008,1152,
%U A291540 1284,1222,1365,1218,1386,1540,1722,1560,1755,1980,2130,2295,2520,2448,2640,2848,3024,3216,3488,3366,3638,3510,3744,4050,4320,4572
%N A291540 a(n) = PrimePi(n) * PrimePi(n^2) - PrimePi(n)^3, where PrimePi = A000720.
%C A291540 All terms are positive except a(1) = a(3) = a(5) = 0 and a(7) = -4, by the PNT with error term for large n and computation for smaller n. In particular, PrimePi(n) * PrimePi(n^2) > PrimePi(n)^3, for n > 7.
%C A291540 For PrimePi(n^3) - PrimePi(n) * PrimePi(n^2), see A291539.
%C A291540 For PrimePi(n^3) - PrimePi(n)^3, see A291538.
%C A291540 For prime(n)^3 - prime(n) * prime(n^2), see A291542.
%F A291540 A291539(n) + a(n) = A291538(n).
%e A291540 a(7) = PrimePi(7) * PrimePi(7^2) - PrimePi(7)^3 = 4 * 15 - 4^3 = -4.
%t A291540 Table[ PrimePi[n] * PrimePi[n^2] - PrimePi[n]^3, {n, 65}]
%o A291540 (PARI) a(n) = primepi(n) * primepi(n^2) - primepi(n)^3; \\ _Michel Marcus_, Sep 10 2017
%Y A291540 Cf. A000720, A123914, A262199, A291440, A291538, A291539, A291541, A291542.
%K A291540 sign
%O A291540 1,4
%A A291540 _Jonathan Sondow_, Aug 25 2017