decompwlj 3D

1 together with numbers of the form p*q^4 and p^9, where p and q are distinct primes

A030628 on the OEIS · family divisor functions

Weight–level plate of 1 together with numbers of the form p*q^4 and p^9, where p and q are distinct primes
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 viewerA030628 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,998
Level class, k > L29,842 · 29.84 %
Weight class, k ≤ L70,156 · 70.16 %
Ties, k = L1
On the level line L = 13,409
Forced level, l ≤ d²196
Range of a(n)1 … 15,938,992
Range of the jump d1 … 1,600
Largest weight k, level L15,936,737, 7,893,895

661 different gaps occur, from 1 to 1,600; the level share is 29.84 %.

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.