[seqfan] Re: Sums of two odd abundant numbers

[mathstutoring]

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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