decompwlj 3D

Number k such that omega(k) = omega(k+3), where omega(k) is the number of distinct prime divisors of k

A063465 on the OEIS · family multiplicative

Weight–level plate of Number k such that omega(k) = omega(k+3), where omega(k) is the number of distinct prime divisors of k
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 viewerA063465 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L16,556 · 16.56 %
Weight class, k ≤ L83,441 · 83.44 %
Ties, k = L30
On the level line L = 19,399
Forced level, l ≤ d²2
Range of a(n)2 … 381,702
Range of the jump d1 … 38
Largest weight k, level L381,697, 190,850

35 different gaps occur, from 1 to 38; the level share is 16.56 %; L = 1 holds 57 % 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.