A105209 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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 A. 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

CROSSREFS

Cf. A000194, A048766.