# [seqfan] Re: A253236

Vladimir Shevelev shevelev at bgu.ac.il
Wed Sep 7 11:37:41 CEST 2016

```Peter's observation is true. Let n>1 and p be the largest
prime divisor of n. If a(n)>0, then a(n)=p. A proof see in
https://www.math.bgu.ac.il/~shevelev/shevelev_et_alJIS2012.pdf
Corollary 23.

Best regards,
Vladimir
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of israel at math.ubc.ca [israel at math.ubc.ca]
Sent: 07 September 2016 09:29
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: A253236

A possibly useful observation: it appears that A253236(n), when nonzero, is
a prime p dividing n such that all other primes that divide n also divide
p-1. Of course this implies that p is the largest prime divisor of n.

Cheers,
Robert

On Sep 6 2016, Peter Lawrence wrote:

>
>A253236    "The unique prime p <= n such that n-th cyclotomic
>polynomial has a root mod p, or 0 if no such p exists."
>
>0, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 0, 13, 7, 0, 2, 17, 3, 19, 5, 7,
>11, 23, 0, 5, 13, 3, 0, 29, 0, 31, 2, 0, 17, 0, 0, 37, 19, 13, 0, 41,
>7, 43, 0, 0, 23, 47, 0, 7, 5, 0, 13, 53, 3, 11, 0, 19, 29, 59, 0, 61,
>31, 0, 2, 0, 0, 67, 17, 0, 0, 71, 0
>
>
>
>a(n), when not 0, appears to be the largest prime divisor of n,
>
>are there any counter-examples to this observation ?
>(my own investigation didn't find any out to n = 10,000)
>
>if not, are there any number theorists that can shed any light on
>this curious phenomenon ?
>
>
>thanks,
>Peter Lawrence.
>
>--
>Seqfan Mailing list - http://list.seqfan.eu/
>
>

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```

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