decompwlj 3D

Nilpotent numbers: n such that every group of order n is nilpotent

A056867 on the OEIS · family multiplicative

Weight–level plate of Nilpotent numbers: n such that every group of order n is nilpotent
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 viewerA056867 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L14,509 · 14.51 %
Weight class, k ≤ L85,489 · 85.49 %
Ties, k = L61
On the level line L = 18,300
Forced level, l ≤ d²2
Range of a(n)1 … 299,109
Range of the jump d1 … 14
Largest weight k, level L299,107, 99,701

11 different gaps occur, from 1 to 14; the level share is 14.51 %; 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.