decompwlj 3D

Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709

A046099 on the OEIS · family multiplicative · also known as Non-cubefree numbers

Weight–level plate of Numbers that are not cubefree. Numbers divisible by a cube greater than 1. Complement of A004709
Click the plate to explore it in 3-D. Weight k across, level L up, both on log scales: blue in the weight class (k ≤ L), orange in the level class (k > L). The dashed diagonal is k = L.
Open in the 3-D viewerA046099 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,057 · 14.06 %
Weight class, k ≤ L85,941 · 85.94 %
Ties, k = L17
On the level line L = 12,584
Forced level, l ≤ d²6
Range of a(n)8 … 594,920
Range of the jump d1 … 8
Largest weight k, level L594,827, 297,391

Divisible by a cube > 1. The level share is 14.06 %; L = 8 holds 37 % of the level class.

The decomposition

Every term of a strictly increasing sequence is written a(n) = k(n)·L(n) + d(n): the jump d = a(n+1) − a(n), the weight k the least divisor of a − d greater than d, the level L = (a − d)/k. A term decomposes when a > 2d; it is in the level class when k > L and in the weight class when k ≤ L. See decompwlj.com and arXiv:0711.0865, or how it works, with worked examples and a live one.