decompwlj 3D

17-smooth numbers: numbers whose prime divisors are all <= 17

A080681 on the OEIS · family smooth

Weight–level plate of 17-smooth numbers: numbers whose prime divisors are all <= 17
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 viewerA080681 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L79,211 · 79.21 %
Weight class, k ≤ L20,787 · 20.79 %
Ties, k = L6
On the level line L = 1154
Forced level, l ≤ d²62,377
Range of a(n)1 … 15,787,406,250
Range of the jump d1 … 3,304,800
Largest weight k, level L14,869,750,279, 20,325,007

39,268 different gaps occur, from 1 to 3,304,800; the level share is 79.21 %; 62.4 % 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.