

A104055


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


1



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
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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 * A216200 A157873 A022870
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



