decompwlj 3D

Numbers that are the sum of 3 positive cubes in more than one way

A008917 on the OEIS · family quadratic form

Weight–level plate of Numbers that are the sum of 3 positive cubes in more than one way
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 viewerA008917 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L34,528 · 34.53 %
Weight class, k ≤ L65,471 · 65.47 %
Ties, k = L2
On the level line L = 17,193
Forced level, l ≤ d²146
Range of a(n)251 … 7,011,775
Range of the jump d1 … 812
Largest weight k, level L7,011,491, 3,504,280

509 different gaps occur, from 1 to 812; the level share is 34.53 %.

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.