decompwlj 3D

Even Niven (or Harshad) numbers: even numbers that are divisible by the sum of their digits

A101814 on the OEIS · family digit rule

Weight–level plate of Even Niven (or Harshad) numbers: even numbers that are divisible by the sum of their digits
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 viewerA101814 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,997
Level class, k > L18,823 · 18.82 %
Weight class, k ≤ L81,174 · 81.18 %
Ties, k = L1
On the level line L = 11
Forced level, l ≤ d²10
Range of a(n)2 … 1,330,470
Range of the jump d2 … 180
Largest weight k, level L665,089, 442,866

45 different gaps occur, from 2 to 180; the level share is 18.82 %.

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.