Divisors concatenated shape a prime

[Eric Angelini]

Sorry for the bad header -- and the old "tail"... I'm not working on my  "normal" computer and quite confused :-/
Best,
É.

________________________________


Hello SeqFans,
could someone check and compute a hundred terms or so of the seq below?
 
4,6,9,21,22,25,33,39,46,49,51,54,...
 
Integers n whose "ordered concatenation" of all divisors (except 1 and n) is a prime.
 
 n     div.         prime
 4 -> 1,2,4     ->    2
 6 -> 1,2,3,6   ->   23
 9 -> 1,3,9     ->    3
21 -> 1,3,7,21  ->   37
22 -> 1,2,11,22 ->  211
25 -> 1,5,25    ->    5
33 -> 1,3,11,33 ->  311
39 -> 1,3,13,39 ->  313
...
26 is not a member :
 
26 -> 1,2,13,26 -> 213 -> 1,3,71,213 -> 371 -> 1,7,53,371 -> 753 -> 1,3,251,753 -> 3251 is prime
 
but 753 will be a member.
 
 
I like 54:
 
54 -> 1,2,3,6,9,18,27,54 -> 23691827 prime
 
Best,
É.
 
-----
 
(I've used Magma to compute the factorization, plus Edwin Clarkk's advice:
 
> [Math-Fun]
>
> (...)
> Use for example the command Divisors(12345678); at this site
>
>   http://magma.maths.usyd.edu.au/calc/
>
> and click on evaluate. You will get
>
> [ 1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 14593, 29186, 43779,
> 87558, 131337, 262674, 685871, 1371742, 2057613, 4115226, 6172839,
> 12345678 ]
>
> Total time: 0.350 seconds, Total memory usage: 6.46MB


 
 
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