decompwlj 3D

Numbers with 14 divisors

A030632 on the OEIS · family multiplicative

Weight–level plate of Numbers with 14 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 viewerA030632 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L28,919 · 28.92 %
Weight class, k ≤ L71,079 · 71.08 %
Ties, k = L3
On the level line L = 11,583
Forced level, l ≤ d²1,021
Range of a(n)192 … 73,803,712
Range of the jump d1 … 6,784
Largest weight k, level L73,770,043, 36,749,983

1,444 different gaps occur, from 1 to 6,784; the level share is 28.92 %; 1.0 % of terms are forced level (l <= d^2).

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.