[seqfan] Re: Strict divisors and digits of a(n)

Charles Greathouse charles.greathouse at case.edu
Sun Dec 1 21:38:48 CET 2013


The English term is "proper divisor". This sequence appears as A132080.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Sun, Dec 1, 2013 at 3:20 PM, Eric Angelini <Eric.Angelini at kntv.be> wrote:

>
> Hello SeqFans,
> I don't know if "strict divisor" (SD) is
> the English translation of the French
> "strict diviseur" -- anyway you will
> understand if I say that the SDs of
> 6 are 1,2 and 3, and (second example),
> the SDs of 28 are 1,2,4,7 and 14.
>
> Now consider S:
>  a(n) will _not_ be part of S if one digit
> of a(n) can be found in one of its SDs:
>
> S=2,3,4,5,6,7,8,9,23,27,29,34,38,...
>
> SDs of the above integers (2nd column):
> 2=1
> 3=1
> 4=1,2
> 5=1
> 6=1,2,3
> 7=1
> 8=1,2,4
> 9=1,3
> 23=1
> 27=1,3,9
> 29=1
> 34=1,2,17
> 38=1,2,19
> ...
> We see that for the above integers,
> no digit at the left of the equal sign
> is repeated at the right of the sign.
>
> My (naive?) question is:
> -- Is S finite?
>
> Best,
> É.
>
>
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