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Numbers of squares in the range [n^3, (n+1)^3].
1

%I #6 Nov 01 2019 16:49:49

%S 2,2,3,3,4,3,4,4,5,5,5,5,5,6,6,6,7,6,6,7,7,7,7,7,8,8,8,8,8,8,8,9,8,9,

%T 9,9,10,9,9,9,10,10,9,10,10,10,11,10,11,11,11,10,11,11,11,12,11,11,12,

%U 11,12,12,12,12,13,12,12,12,13,12,13,12,13,13,13,13,13,13,14,13,14,14,14

%N Numbers of squares in the range [n^3, (n+1)^3].

%e a(0)=2 because between the cubes 0 and 1 there are exactly 2 squares, {0,1}.

%e a(1)=2 because between the cubes 1 and 8 there are exactly 2 squares, {1,4}.

%t Table[ Floor[Sqrt[(n + 1)^3] - Ceiling[Sqrt[n^3]]] + 1, {n, 0, 82}] (* _Ray Chandler_, Jan 09 2005 *)

%K easy,nonn

%O 0,1

%A _Giovanni Teofilatto_, Dec 27 2004

%E Corrected and extended by _Ray Chandler_, Jan 09 2005