[seqfan] Re: Sums of two odd abundant numbers
mathstutoring
mathstutoring at ntlworld.com
Mon Nov 23 16:29:12 CET 2009
References duly added
Ant
----- Original Message -----
From: "Charles Greathouse" <charles.greathouse at case.edu>
To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Sent: Monday, November 23, 2009 2:50 PM
Subject: [seqfan] Re: Sums of two odd abundant numbers
See also A048242. (Ant, want to add your references to that sequence?)
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
On Sat, Nov 21, 2009 at 6:29 AM, mathstutoring
<mathstutoring at ntlworld.com> wrote:
> It is possible to express any even number larger than 46 and any odd
> number
> larger than 20161 as the sum of two abundant numbers. See, for example,
>
> Parkin, Thomas R.; Lander, Leon J.; Abundant numbers, Aerospace
> Corporation,
> Los Angeles, 1964, 119 unnumbered pages. Copy deposited in UMT file.
>
> Pirani, F. A. E.; Problems For Solution "E903", The American Mathematical
> Monthly, Vol. 57, No. 2, (February 1950), p. 113.
>
> Pirani, F. A. E.; Moser, Leo; Selfridge, John; E903, The American
> Mathematical Monthly, Vol. 57, No. 8. (October 1950), pp. 561-562.
>
> Review of "Abundant Numbers by Thomas R. Parkin and Leon J. Lander",
> Mathematics of Computation, Vol. 19, No. 90. (April 1965), p. 334.
>
> Ant
>
> ----- Original Message -----
> From: "William Marshall" <w.r.marshall at actrix.co.nz>
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Sent: Friday, November 20, 2009 9:24 PM
> Subject: [seqfan] Sums of two odd abundant numbers
>
>
>> The sequence of even numbers which are the sum of two odd abundant
>> numbers begins:
>>
>> 1890, 2520, 3150, 3780, 4410, 5040, 5670, 6300, 6720, 6930, 7350, 7380,
>> 7560, 7770, 7980, 8010, 8190, 8370, 8400, 8610, 8640, 8820, 9000, 9030,
>> 9240, 9270, 9360, 9450, 9630, 9660, 9870, 9900, 9990, 10080, 10260,
>> 10290, 10500, 10530, 10620, 10710
>>
>> Every even number >= 3706141025766237065507279802221127212928 is the sum
>> of two odd abundant numbers. (In fact, they are the sum of odd multiples
>> of the coprime odd abundants 34050375 and
>> 54421442938406405273270633223449.)
>>
>> What is the largest even number which is not the sum of two odd abundant
>> numbers (and therefore the largest even number which does not appear in
>> the above sequence)? If that is too hard, how far can the upper bound be
>> reduced, and what is the largest known even number which is not the sum
>> of two odd abundant numbers?
>>
>>
>>
>> _______________________________________________
>>
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>
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