[seqfan] Mystery: trios in A046346.

[israel at math.ubc.ca]

A046346 is "Composite numbers that are divisible by the sum of their prime 
factors (counted with multiplicity)".

Noticing that there are pairs x,x+2 both in A046346, J.M. Bergot and I 
jointly submitted A309310, which is "Intersection of A046346 and 
(A046346-2)". I noticed that A046346 also contained a trio x,x+2,x+4, 
namely 646, 648, 650, which I thought to be an interesting coincidence. 
Well, just now I was constructing a b-file for A309310: not so easy because 
the numbers get quite sparse. To get A309310(200) I had to go all the way 
up to 192678462. Thus it seems to me astonishing that there's another trio: 
38104990, 38104992, and 38104994 are all members of A046346.

Can anyone make sense of this?  Are there more trios?  Infinitely many?

Cheers,
Robert