[seqfan] Re: A093893 Subsequence
Robert Gerbicz
robert.gerbicz at gmail.com
Sun May 24 15:50:28 CEST 2009
2009/5/24 Leroy Quet <q1qq2qqq3qqqq at yahoo.com>
>
> Consider sequence A093893,
> This is the list of positive integers n such that the partial sum of any 2
> or more divisors of n is composite.
>
> What I wonder about is the subsequence, which doesn't seem to be in the
> EIS, where the nth term is the smallest term of A093893 with exactly n
> divisors.
>
> (Starts at a(2).)
>
> 3, 49, 87, etc.
>
> It seems that it is very unlikely that this sequence is infinite, or even
> that it is not short.
>
> Can it be proved that this sequence is finite or infinite?
>
> Thanks,
> Leroy Quet
>
>
>
>
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>
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>
You can try the easiest such numbers: N=p^(n-1), where p is prime, it has
got n divisors, and using prime number's theorem it is provable, that if the
partial sum's of the divisors are "random" and p is "large" then by high
probability all such sums are composite. So the sequence is infinite.
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