[seqfan] Re: Sums of two odd abundant numbers
mathstutoring
mathstutoring at ntlworld.com
Sat Nov 21 12:29:53 CET 2009
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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