decompwlj 3D

Numbers with 28 divisors

A137491 on the OEIS · family multiplicative

Weight–level plate of Numbers with 28 divisors
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 viewerA137491 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L25,469 · 25.47 %
Weight class, k ≤ L74,531 · 74.53 %
Ties, k = L4
On the level line L = 11,088
Forced level, l ≤ d²495
Range of a(n)960 … 33,301,312
Range of the jump d1 … 3,200
Largest weight k, level L33,298,537, 16,454,623

1,048 different gaps occur, from 1 to 3,200; the level share is 25.47 %; L = 64 holds 38 % 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.