# [seqfan] Sums of two odd abundant numbers

William Marshall w.r.marshall at actrix.co.nz
Fri Nov 20 22:24:48 CET 2009

```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?

```