0,3

The asymptotic density of cubefree integers is the reciprocal of Apery's constant 1/zeta(3) = 0.83190737258... The number of cubefree integers not exceeding N is thus roughly N/zeta(3). When N is a power of 10, this sequence gives the difference between the actual number (A160112) and that linear estimate (rounded to the nearest integer).

G. P. Michon, Reciprocal of Apery's constant.

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

Eric Weisstein's World of Mathematics, Cubefree.

a(n) = A160112(n)-round(10^n/zeta(3))

A004709 (cube-free integers). A160112 & A160113 (counting cubefree integers).

Sequence in context: A003992 A118345 A118350 this_sequence A109970 A116088 A136501

Adjacent sequences: A160111 A160112 A160113 this_sequence A160115 A160116 A160117

easy,sign

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