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<DIV>Leroy is quite correct.</DIV>
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<DIV>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).</DIV>
<DIV> </DIV>
<DIV>According to A047802, the first abundant number prime to both 2 and 3 is 5391411025.</DIV>
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<DIV>(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.)</DIV>
<DIV> </DIV>
<DIV>Franklin T. Adams-Watters<BR>16 W. Michigan Ave.<BR>Palatine, IL 60067<BR>847-776-7645</DIV> <BR>-----Original Message-----<BR>From: Leroy Quet <A href="mailto:qq-quet@mindspring.com">qq-quet@mindspring.com</A><BR><BR>
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<DIV class=AOLPlainTextBody id=AOLMsgPart_0_2a7cf84d-a7b0-4c05-b6c4-b110d78a1c49><PRE><TT>>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.
:)
</TT></PRE></DIV></DIV></DIV>
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