decompwlj 3D

Hati numbers: of form 2^i*3^j*k, i+j even, (k,6)=1

A036668 on the OEIS · family multiplicative

Weight–level plate of Hati numbers: of form 2^i*3^j*k, i+j even, (k,6)=1
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 viewerA036668 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L13,077 · 13.08 %
Weight class, k ≤ L86,922 · 86.92 %
Ties, k = L3
On the level line L = 19,773
Forced level, l ≤ d²0
Range of a(n)1 … 171,436
Range of the jump d1 … 4
Largest weight k, level L171,403, 85,713

The gaps are 1, 2, 3 and 4; the level share is 13.08 %; L = 1 holds 75 % 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.