0,2

An alternate definition specifying "less than 10^n" would yield the same sequence except for the first 3 terms: 0, 8, 84, 833, 8319, etc. (since powers of 10 beyond 1000 are not cubefree anyhow).

The limit of a(n)/10^n is the inverse of Apery's constant, 1/zeta(3), whose digits are given by A088453.

G. P. Michon, Table of n, a(n) for = n=0..29

G. P. Michon, On the number of cubefree integers not exceeding N.

a(n) = Sum for i=1 to 10^(n/3) of A008683(i)*floor(10^n/i^3)

a(0)=1 because 1 <= 10^0 is not a multiple of the cube of a prime.

a(1)=9 because the 9 numbers 1,2,3,4,5,6,7,9,10 are cubefree; 8 is not.

a(2)=85 because there are 85 cubefree integers equal to 100 or less.

a(3)=833 because there are 833 cubefree integers below 1000 (which is not cube-free itself).

Table[ Sum[ MoebiusMu[x]*Floor[10^n/(x^3)], {x, 10^(n/3)}], {n, 0, 18}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), May 27 2009]

A004709 (cube-free numbers). A088453 (limit of the string of digits). A160113 (binary counterpart for cubefree integers). A071172 & A053462 (decimal counterpart for squarefree integers). A143658 (binary counterpart for squarefree integers).

Adjacent sequences: A160109 A160110 A160111 this_sequence A160113 A160114 A160115

Sequence in context: A024118 A015580 A163308 this_sequence A108427 A152106 A142982

easy,nice,nonn

Gerard P. Michon (g.michon(AT)att.net), May 02 2009, May 06 2009