decompwlj 3D

Even squarefree numbers

A039956 on the OEIS · family multiplicative

Weight–level plate of Even squarefree numbers
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 viewerA039956 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L17,469 · 17.47 %
Weight class, k ≤ L82,528 · 82.53 %
Ties, k = L0
On the level line L = 11
Forced level, l ≤ d²2
Range of a(n)2 … 493,490
Range of the jump d4 … 24
Largest weight k, level L246,739, 98,694

6 different gaps occur, from 4 to 24; the level share is 17.47 %; L = 2 holds 78 % of the level class; there are no ties.

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.