decompwlj 3D

Numbers k with at least one divisor d>1 such that d+1 also divides k

A088723 on the OEIS · family divisor functions

Weight–level plate of Numbers k with at least one divisor d>1 such that d+1 also divides 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 viewerA088723 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,459 · 14.46 %
Weight class, k ≤ L85,539 · 85.54 %
Ties, k = L1
On the level line L = 10
Forced level, l ≤ d²4
Range of a(n)6 … 450,606
Range of the jump d2 … 6
Largest weight k, level L225,289, 149,906

The gaps are 2, 4 and 6; the level share is 14.46 %; L = 6 holds 42 % 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.