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A097449
If n is a cube, replace it with the cube root of n.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Aug 23 2004
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved