A105209 Nearest integer to the cube root of n.

1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

1,4

References

Erwin Voellmy, Fünfstellige Logarithmen und Zahlentafeln, Orell Füssli Verlag, Zürich (1962).

Links

Table of n, a(n) for n=1..105.

Seung-Jin Bang, Problem 10212, The American Mathematical Monthly, Vol. 99, No. 4 (1992), p. 361, Nearest Integer Zeta Functions, solution to Problem 10212, ibid., Vol. 101, No. 6 (1994), pp. 579-580.

Formula

Sum_{n>=1} 1/a(n)^s = 3*zeta(s-2) + zeta(s)/4^s, for s > 3 (Seung-Jin Bang, 1992). - Amiram Eldar, Oct 31 2020

Example

a(16) = 3 because 16^(1/3) = 2.519842...

Maple

for n from 1 to 200 do printf(`%d, `, round(n^(1/3))) od: # James Sellers, Apr 21 2005

Mathematica

Round[Surd[Range[110], 3]] (* Harvey P. Dale, Feb 28 2015 *)

Prog

(PARI) a(n) = round(n^(1/3)); \\ Michel Marcus, Aug 19 2016
(Python)
from sympy import integer_nthroot
def A105209(n): return (m:=integer_nthroot(n, 3)[0])+((n<<3)>=((m<<1)+1)**3) # Chai Wah Wu, Jun 06 2025

Crossrefs

Cf. A000194, A048766.

Sequence in context: A001069 A156877 A110591 * A179076 A095861 A382692

Adjacent sequences: A105206 A105207 A105208 * A105210 A105211 A105212

Keyword

easy,nonn

Author

Pahikkala Jussi, Apr 13 2005

Extensions

More terms from James Sellers, Apr 21 2005

Status

approved