A104055 Number of numbers 0 <= i <= n such that i is a square or a cube (or both).

1, 2, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13

Offset

0,2

Comments

Sixth powers are counted only once (0 and 1 are both squares and cubes, for example, but they are not counted twice).

Links

Table of n, a(n) for n=0..103.

Formula

a(n) = 1 + floor(n^(1/2)) + floor(n^(1/3)) - floor(n^(1/6)). - N. J. A. Sloane, Mar 16 2005

Example

a(9)=5 because we have 0,1,4,8 and 9.

Maple

seq(1+floor(evalf(n^(1/2)))+floor(evalf(n^(1/3)))-floor(evalf(n^(1/6))), n=0..94); # Emeric Deutsch

Mathematica

Rest[Accumulate[Table[Which[IntegerQ[Sqrt[n]], 1, IntegerQ[Surd[n, 3]], 1, True, 0], {n, 0, 150}]]] (* Harvey P. Dale, Jun 24 2017 *)

Prog

(PARI) a(n)=sqrtint(n)+sqrtnint(n, 3)-sqrtnint(n, 6) \\ Charles R Greathouse IV, Jun 25 2017

Crossrefs

Cf. A104058.

Sequence in context: A189575 A216503 A216672 * A352100 A216200 A157873

Adjacent sequences: A104052 A104053 A104054 * A104056 A104057 A104058

Keyword

easy,nonn

Author

Giovanni Teofilatto, Mar 02 2005

Extensions

More terms from Emeric Deutsch, Mar 24 2005

Corrected by Harvey P. Dale, Jun 24 2017

Definition revised by N. J. A. Sloane, Jun 25 2017

Status

approved