A160114 Fluctuations of the number of cubefree integers not exceeding 10^n.

0, 1, 2, 1, 0, -1, 3, 7, -10, -1, -7, -14, -59, 21, 34, -15, 103, -104, 302, -38, -514, -290, 1130, 504, 2466, 6813, -1854, 1590, -4879, 3963, -4767, -22709

Offset: 0

Author

Gerard P. Michon, May 06 2009

Keywords

• easy
• sign

Comments

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).

Links

• 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.

Crossrefs

A004709 (cubefree integers). A160112 & A160113 (counting cubefree integers).

Formula

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

Extensions

a(30)-a(31) from Chai Wah Wu, Aug 08 2024