decompwlj 3D

Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9

A195093 on the OEIS · family multiplicative

Weight–level plate of Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9
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 viewerA195093 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L22,790 · 22.79 %
Weight class, k ≤ L77,208 · 77.21 %
Ties, k = L9
On the level line L = 195
Forced level, l ≤ d²2,103
Range of a(n)1,024 … 135,240,000
Range of the jump d1 … 9,728
Largest weight k, level L133,679,881, 48,390,655

2,302 different gaps occur, from 1 to 9,728; the level share is 22.79 %; 2.1 % of terms are forced level (l <= d^2).

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.