Harshad numbers which terminate in their digital sum
Open in the 3-D viewerA070938 on the OEIS
| Terms | 100,000 (n = 1 … 100,000) |
|---|---|
| Decomposable (a > 2d) | 99,996 |
| Level class, k > L | 25,258 · 25.26 % |
| Weight class, k ≤ L | 74,738 · 74.74 % |
| Ties, k = L | 3 |
| On the level line L = 1 | 4,305 |
| Forced level, l ≤ d² | 886 |
| Range of a(n) | 1 … 30,374,120 |
| Range of the jump d | 1 … 909 |
| Largest weight k, level L | 30,372,323, 15,186,612 |
48 different gaps occur, from 1 to 909; the level share is 25.26 %.
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.