decompwlj 3D

Numbers that are the product of exactly three (not necessarily distinct) primes

A014612 on the OEIS · family multiplicative · also known as 3-almost primes

Weight–level plate of Numbers that are the product of exactly three (not necessarily distinct) primes
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 viewerA014612 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L15,789 · 15.79 %
Weight class, k ≤ L84,209 · 84.21 %
Ties, k = L59
On the level line L = 110,143
Forced level, l ≤ d²5
Range of a(n)8 … 395,085
Range of the jump d1 … 34
Largest weight k, level L395,023, 197,514

Omega(n) = 3. The gaps stay between 1 and 34 here. The level share is 15.79 %, beside the semiprimes' 15.71 %, and L = 1 carries 64 % 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.