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Number of primes in the interval [ sqrt(n^3) , sqrt((n+1)^3) ].
1

%I #23 Aug 27 2023 15:20:57

%S 1,2,1,1,1,1,1,1,2,0,2,1,1,1,2,1,2,1,2,0,3,2,1,0,2,2,0,2,2,1,3,0,3,1,

%T 1,1,3,2,1,1,3,2,1,1,2,2,1,1,3,1,2,2,1,2,2,1,3,2,3,1,2,2,2,2,0,2,1,3,

%U 1,2,3,3,1,3,3,1,2,2,1,2,2,2,3,1,2,2,2

%N Number of primes in the interval [ sqrt(n^3) , sqrt((n+1)^3) ].

%t Table[PrimePi[(n+1)^(3/2)] - PrimePi[n^(3/2)], {n, 87}] (* _T. D. Noe_, Oct 14 2011 *)

%t Differences[Table[PrimePi[Sqrt[n^3]],{n,90}]] (* _Harvey P. Dale_, Aug 27 2023 *)

%Y Cf. A014085, A000720.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Sep 04 2011

%E Corrected by R. J. Mathar, Sep 04 2011