A117491 - OEIS

A117491

The number of primes between n and n^3 (with n and n^3 excluded).

%I #14 Sep 07 2024 08:54:02

%S 0,3,7,16,27,44,64,93,125,164,212,264,321,394,470,558,649,758,874,999,

%T 1139,1290,1448,1624,1812,2011,2218,2451,2697,2951,3217,3501,3806,

%U 4126,4472,4810,5182,5567,5983,6401,6837,7295,7775,8279,8796,9347,9901,10484

%N The number of primes between n and n^3 (with n and n^3 excluded).

%H Amiram Eldar, <a href="/A117491/b117491.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 3: between 3+1 = 4 and 3^3-1 = 26 there are the following primes: 5, 7, 11, 13, 17, 19, 23. Therefore the number of primes is 7.

%p P:=proc(n) local i,j,np; for i from 1 by 1 to n do np:=0; for j from i+1 by 1 to i^3-1 do if isprime(j) then np:=np+1; fi; od; print(np); od; end: P(100);

%t Table[PrimePi[n^3]-PrimePi[n],{n,50}] (* _Harvey P. Dale_, Nov 08 2012 *)

%Y Cf. A060715, A117490.

%K easy,nonn

%O 1,2

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Mar 22 2006