First even term

[franktaw at netscape.net]

Leroy is quite correct.
 
The first abundant number relatively prime to 10 is 81081.  The first term of A085493 with a(n)+1 relatively prime to 10 is thus 81080 (all divisors of 81081 except 1, 33, 429, and 81081 itself).
 
According to A047802, the first abundant number prime to both 2 and 3 is 5391411025.
 
(Theoretically, A085493 could contain one less than an odd number with sigma(n)=2n-1, but no such numbers are known.  Any such number would have to be a square.)
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
 
-----Original Message-----
From: Leroy Quet qq-quet at mindspring.com


>Even elements of A085493:
>
>944 1574 2204 2834 3464 4094 4724 5354 5774 5984 6434 6614 6824 7244
>7424 7874 8084 8414 8504 8924 9134 9554 9764 10394 11024 11654 12284
>12704 12914 13544 14174 14804 15014 15434 16064 16694 17324 17954 18584
>
>My values show a disturbing tendency to end in the digit 4 that is not 
>apparent 
>from the definition.

Hmmm...
I believe the ending-in-4 pattern can be explained simply by the fact 
that (n+1) is an odd multiple of 5.

I would guess without checking that many many terms of the sequence are 
congruent to -1 mod 3 as well.

And the abundance of odd terms in A085493 is explained by the fact that 
the terms + 1 are multiples of 2.

So, looking ahead we should probably eventually come across even terms 
which do not end in 4.
:)
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