A097449 If n is a cube, replace it with the cube root of n.

0, 1, 2, 3, 4, 5, 6, 7, 2, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 3, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset

0,3

Links

Table of n, a(n) for n=0..74.

Formula

Sum_{n>=1} (-1)^(n+1)/n = 2*log(2) - 3*zeta(3)/4 = A016627 - A197070. - Amiram Eldar, Jul 07 2024

Example

The 9th integer is 8 so a(9) = 8^(1/3) = 2.

Mathematica

rcr[n_]:=Module[{crn=Power[n, (3)^-1]}, If[IntegerQ[crn], crn, n]]; Array[ rcr, 80, 0] (* Harvey P. Dale, Jan 28 2012 *)

Prog

(PARI) iscube(n) = { local(r); r = n^(1/3); if(floor(r+.5)^3== n, 1, 0) }
replcube(n) = { for(x=0, n, if(iscube(x), y=x^(1/3), y=x); print1(floor(y)", ")) }
(PARI) a(n)=ispower(n, 3, &n); n \\ Charles R Greathouse IV, Oct 27 2011

Crossrefs

Cf. A016627, A097448, A197070.

Sequence in context: A091733 A066990 A365296 * A104415 A071074 A279648

Adjacent sequences: A097446 A097447 A097448 * A097450 A097451 A097452

Keyword

nonn,easy

Author

Cino Hilliard, Aug 23 2004

Extensions

Corrected by T. D. Noe, Oct 25 2006

Status

approved