[seqfan] Interesting horizontal line in https://oeis.org/A369657/graph

[Thomas Scheuerle]

Dear sequence fans,

In A369657 from Antti Katunen, is 
A369657(n) = A356253(n) - A003415(n).
A356253(n) is the greatest number we may obtain by applying elementary symmetric functions onto the prime factors of n with multiplicity.
A003415(n) is the arithmetic derivative of n.

The horizontal line we may observe in the graph https://oeis.org/A369657/graph, is essentially caused by A369657(2^5*prime(n)) = 48.

We can proof that this holds:
A003415(2^5*p) =  2^5*p*(5/2 + 1/p)
2^5*p*(5/2 + 1/p) + 48 =  80*p+80

Regarding  A356253(2^5*p):
(2-x)^5*(p-x) = x^6 -(p+10)*x^5 + (10*p+40)*x^4 - (40*p-80)*x^3 + (80*p+80)*x^2 - (80*p+32)*x + 32*p
The biggest factor is (80*p+80).

The mystery for me is, is this the only such horizontal line in this graph?
I was not able to find another such relation which surprises me.
What do you think about this?

best regards

Thomas Scheuerle