decompwlj 3D

Numbers with exactly 64 divisors

A172443 on the OEIS · family multiplicative

Weight–level plate of Numbers with exactly 64 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 viewerA172443 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L27,120 · 27.12 %
Weight class, k ≤ L72,880 · 72.88 %
Ties, k = L1
On the level line L = 1107
Forced level, l ≤ d²240
Range of a(n)7,560 … 8,818,936
Range of the jump d1 … 1,728
Largest weight k, level L8,775,997, 4,370,827

540 different gaps occur, from 1 to 1,728; the level share is 27.12 %.

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.