decompwlj 3D

Squarefree semiprimes: Numbers that are the product of two distinct primes

A006881 on the OEIS · family multiplicative · also known as Squarefree semiprimes

Weight–level plate of Squarefree semiprimes: Numbers that are the product of two 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 viewerA006881 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L15,721 · 15.72 %
Weight class, k ≤ L84,278 · 84.28 %
Ties, k = L41
On the level line L = 19,561
Forced level, l ≤ d²5
Range of a(n)6 … 460,121
Range of the jump d1 … 47
Largest weight k, level L460,051, 230,058

Products of two distinct primes. The plane is the semiprimes' almost exactly (15.72 % level against 15.71 %).

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.