decompwlj 3D

Sum of a square and a nonnegative cube

A022549 on the OEIS · family powers

Weight–level plate of Sum of a square and a nonnegative cube
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 viewerA022549 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,996
Level class, k > L24,755 · 24.76 %
Weight class, k ≤ L75,241 · 75.24 %
Ties, k = L37
On the level line L = 17,614
Forced level, l ≤ d²4
Range of a(n)0 … 1,363,072
Range of the jump d1 … 149
Largest weight k, level L1,362,731, 681,205

120 different gaps occur, from 1 to 149; the level share is 24.76 %; L = 1 holds 31 % 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.