decompwlj 3D

Sphenic numbers: products of 3 distinct primes

A007304 on the OEIS · family multiplicative · also known as Sphenic numbers

Weight–level plate of Sphenic numbers: products of 3 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 viewerA007304 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)99,999
Level class, k > L17,039 · 17.04 %
Weight class, k ≤ L82,960 · 82.96 %
Ties, k = L39
On the level line L = 110,570
Forced level, l ≤ d²8
Range of a(n)30 … 486,809
Range of the jump d1 … 44
Largest weight k, level L486,769, 243,392

Products of three distinct primes. The level share is 17.04 %, against 15.72 % for the squarefree semiprimes.

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.