decompwlj 3D

13-rough numbers: positive integers that have no prime factors less than 13

A008365 on the OEIS · family forced divisor

Weight–level plate of 13-rough numbers: positive integers that have no prime factors less than 13
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 viewerA008365 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L15,513 · 15.51 %
Weight class, k ≤ L84,486 · 84.49 %
Ties, k = L15
On the level line L = 15,656
Forced level, l ≤ d²5
Range of a(n)1 … 481,249
Range of the jump d2 … 14
Largest weight k, level L481,207, 160,415

7 different gaps occur, from 2 to 14; the level share is 15.51 %; L = 3 holds 37 % 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.