decompwlj 3D

Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010

A179188 on the OEIS · family divisor functions

Weight–level plate of Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010
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 viewerA179188 on the OEIS
Terms100,000 (n = 1 … 100,000)
Decomposable (a > 2d)100,000
Level class, k > L37,959 · 37.96 %
Weight class, k ≤ L62,041 · 62.04 %
Ties, k = L5
On the level line L = 12,417
Forced level, l ≤ d²228
Range of a(n)24 … 22,815,867
Range of the jump d1 … 2,783
Largest weight k, level L22,815,361, 11,301,040

1,400 different gaps occur, from 1 to 2,783; the level share is 37.96 %.

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.