Cubefree

A number is said to be cubefree if its Prime decomposition contains no tripled factors. All Primes are thereforetrivially cubefree. The cubefree numbers are 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, ... (Sloane's A004709). Thecubeful numbers (i.e., those that contain at least one cube) are 8, 16, 24, 27, 32, 40, 48, 54, ... (Sloane's A046099). Thenumber of cubefree numbers less than 10, 100, 1000, ... are 9, 85, 833, 8319, 83190, 831910, ..., and their asymptoticdensity is , where is the Riemann Zeta Function.

References

Sloane, N. J. A.A004709 andA046099 in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.

• Liouville Measure
• Liouville Number
• Liouville Polynomial Identity
• Liouville-Roth Constant
• Liouville's Boundedness Theorem
• Liouville's Conformality Theorem
• Liouville's Conic Theorem
• Liouville's Constant
• Liouville's Elliptic Function Theorem
• Liouville Space
• Liouville's Phase Space Theorem
• Liouville's Rational Approximation Theorem
• Liouville's Sphere-Preserving Theorem
• Lipschitz Condition
• Lipschitz Function
• Lipschitz's Integral
• Lissajous Curve
• Lissajous Figure
• List
• Lituus
• Lituus Inverse Curve
• LLL Algorithm
• Ln
• Lobachevsky-Bolyai-Gauss Geometry
• Lobachevsky's Formula