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

0,11

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.

Formula

a(n) = A160113(n)-round(2^n/zeta(3))

Crossrefs

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

Sequence in context: A340146 A340143 A255920 * A139365 A071479 A257398

Adjacent sequences: A160112 A160113 A160114 * A160116 A160117 A160118

Keyword

easy,sign

Author

Gerard P. Michon, May 06 2009

Status

approved