[seqfan] Re: Is this right? smallest prime factor of smaller of amicable pair
kohmoto
zbi74583.boat at orange.zero.jp
Tue Aug 17 07:41:46 CEST 2010
The observation about smallest prime factor is known as "Bratley and
Mckay's conjecture"
See MathWorld.
http://mathworld.wolfram.com/AmicablePair.html
Yasutoshi
--------------------------------------------------
From: "Jonathan Post" <jvospost3 at gmail.com>
Sent: Tuesday, August 17, 2010 2:22 AM
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Subject: [seqfan] Re: Is this right? smallest prime factor of smaller of
amicable pair
> I understand Charles Greathouse's point. The comment could say that
> an exception, to values being 2 or 3, but not necessarily the smallest
> exception...
>
> On Mon, Aug 16, 2010 at 10:15 AM, Charles Greathouse
> <charles.greathouse at case.edu> wrote:
>> Unfortunately it's not currently feasible to determine the index of
>> that value; conservatively, it would take 10^17 machine instructions
>> on a computer with a very large memory to determine by sieving.
>>
>> Charles Greathouse
>> Analyst/Programmer
>> Case Western Reserve University
>>
>> ---------- Forwarded message ----------
>> From: Jonathan Post <jvospost3 at gmail.com>
>> Date: Mon, Aug 16, 2010 at 11:43 AM
>> Subject: [seqfan] Re: Is this right? smallest prime factor of smaller
>> of amicable pair
>> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>>
>>
>> Thank you both, Tony and Charles! I always like it when a sequence
>> that seems stuck in the mud digs its tires out, and climbs onto higher
>> ground.
>>
>> So there should be a comment akin to:
>> "The first value other than 2 or 3 was found by Charles Greathouse as
>> a(?) = 5480828320492525 = 5^2 * 7^2 * 11 * 13 * 17 * 19 * 23 * 31 * 103 *
>> 1319
>>
>> On Sun, Aug 15, 2010 at 11:48 PM, Charles Greathouse
>> <charles.greathouse at case.edu> wrote:
>>> It doesn't hold: 5480828320492525.
>>>
>>> Charles Greathouse
>>> Analyst/Programmer
>>> Case Western Reserve University
>>>
>>> On Mon, Aug 16, 2010 at 2:24 AM, T. D. Noe <noe at sspectra.com> wrote:
>>>> At 11:14 PM -0700 8/15/10, Jonathan Post wrote:
>>>>>2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 3, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2,
>>>>>2, 2, 2, 2, 2, 2, 3, 2, 2
>>>>>smallest prime factor of smaller of amicable pair
>>>>>a(n) = A020639(A002025(n)) = Lpf(A002025(n)) =
>>>>>sigma(A002025(n))-A002025(n).
>>>>>Must always be 2 or 3?
>>>>
>>>>
>>>> It is true for all the terms in the b-file for A063990, which includes
>>>> the
>>>> larger of the amicable pair also.
>>>>
>>>> Tony
>>>>
>>>>
>>>>
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