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

Author

Cino Hilliard, Aug 23 2004

Keywords

• nonn
• easy

Examples

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

Crossrefs

Cf. A016627, A097448, A197070.

Programs

Mathematica

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

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

Formula

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

Extensions

Corrected by T. D. Noe, Oct 25 2006