Biquadratefree numbers: numbers that are not divisible by any 4th power greater than 1
Open in the 3-D viewerA046100 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,998 |
| Level class, k > L | 9,928 · 9.93 % |
| Weight class, k ≤ L | 90,070 · 90.07 % |
| Ties, k = L | 63 |
| On the level line L = 1 | 9,919 |
| Forced level, l ≤ d² | 0 |
| Range of a(n) | 1 … 108,232 |
| Range of the jump d | 1 … 4 |
| Largest weight k, level L | 108,217, 54,115 |
The gaps are 1, 2, 3 and 4; the level share is 9.93 %; L = 1 holds 100 % 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.