decompwlj 3D

Numbers k such that omega(k) = omega(k+2), where omega(k) is the number of distinct prime divisors of k

A063464 on the OEIS · family multiplicative

Weight–level plate of Numbers k such that omega(k) = omega(k+2), 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 viewerA063464 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,699 · 14.70 %
Weight class, k ≤ L85,299 · 85.30 %
Ties, k = L38
On the level line L = 17,998
Forced level, l ≤ d²3
Range of a(n)2 … 341,253
Range of the jump d1 … 37
Largest weight k, level L341,233, 170,625

31 different gaps occur, from 1 to 37; the level share is 14.70 %; L = 1 holds 54 % 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.