decompwlj 3D

Numbers k whose largest divisor <= sqrt(k) equals 7

A162527 on the OEIS · family divisor functions

Weight–level plate of Numbers k whose largest divisor <= sqrt(k) equals 7
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 viewerA162527 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L23,105 · 23.11 %
Weight class, k ≤ L76,895 · 76.89 %
Ties, k = L2
On the level line L = 12
Forced level, l ≤ d²90
Range of a(n)49 … 9,097,207
Range of the jump d7 … 798
Largest weight k, level L1,299,061, 606,403

54 different gaps occur, from 7 to 798; the level share is 23.11 %; L = 7 holds 32 % 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.