[seqfan] Re: Mystery: trios in A046346.

[Giovanni Resta]

Up to 3*10^12 I only found another such triple starting at 590269019100.

Giovanni


On 7/23/19 3:32 AM, israel at math.ubc.ca wrote:
> 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
> 
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