decompwlj 3D

Semiprimes where the larger prime factor is greater than the square of the smaller prime factor, short: semiprimes p*q, p^2 < q

A138511 on the OEIS · family multiplicative

Weight–level plate of Semiprimes where the larger prime factor is greater than the square of the smaller prime factor, short: semiprimes p*q, p^2 < q
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 viewerA138511 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L18,204 · 18.20 %
Weight class, k ≤ L81,795 · 81.80 %
Ties, k = L47
On the level line L = 110,632
Forced level, l ≤ d²4
Range of a(n)10 … 617,014
Range of the jump d1 … 70
Largest weight k, level L616,951, 308,490

53 different gaps occur, from 1 to 70; the level share is 18.20 %; L = 1 holds 58 % 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.