decompwlj 3D

Products of exactly four distinct primes

A046386 on the OEIS · family multiplicative · also known as Products of four distinct primes

Weight–level plate of Products of exactly four 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 viewerA046386 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L21,021 · 21.02 %
Weight class, k ≤ L78,978 · 78.98 %
Ties, k = L8
On the level line L = 15,023
Forced level, l ≤ d²26
Range of a(n)210 … 1,068,585
Range of the jump d1 … 144
Largest weight k, level L1,068,407, 534,292

Products of four distinct primes. The level share is 21.02 %; L = 2 holds 34 % 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.