decompwlj 3D

Numbers that are products of 4 primes

A014613 on the OEIS · family multiplicative · also known as 4-almost primes

Weight–level plate of Numbers that are products of 4 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 viewerA014613 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L16,889 · 16.89 %
Weight class, k ≤ L83,109 · 83.11 %
Ties, k = L20
On the level line L = 16,053
Forced level, l ≤ d²9
Range of a(n)16 … 511,725
Range of the jump d1 … 43
Largest weight k, level L511,603, 255,829

Omega(n) = 4. The level share is 16.89 %. The lines L = 1 and L = 2 are nearly equal (36 % and 33 % of the level class); 65 % of the terms are even.

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.