A160115 Fluctuations of the number of cubefree integers not exceeding 2^n.

0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 0, -1, -1, 1, 2, 0, -1, 0, 2, 6, 1, 2, 7, 5, -1, -7, -4, 4, -7, -21, -7, -2, 30, 2, 14, -8, 7, -1, -7, -12, -1, 21, 28, 7, -29, -33, -76, -88, 15, 47, 58, -51, -112, 293, 122, 316, -96, -42, -259, 140, -111, 6, -790, -342, 146, 395, 1087

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 2, this sequence gives the difference between the actual number (A160113) and that linear estimate (rounded to the nearest integer).

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..99
• 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) = A160113(n)-round(2^n/zeta(3))