When is A111075(n) Odd?

[Paul D. Hanna]

Seqfans,
      To clarify, I should have stated my conjecture as the  
UNION of (i) and (ii) (by using "or", not "and"), like so: 
 
Conjecture: A111075(n) is odd whenever: 
(i)  n = m^2 for all m>=1 such that 3 does not divide m, or
(ii)  n = 3*A028982(m) for all m>=1.
 
Also, A028982 gives "Union of nonzero squares and twice squares."
 
Underneath it all, this may be trivial, yet for now it seems mysterious 
why the number 3 and the squares would determine when A111075 is odd ...
 
If someone can support the conjecture, they are welcome to submit 
the new sequence: "n for which A111075 is odd." 
 
Thanks,
      Paul
 
On Wed, 12 Oct 2005 00:44:40 -0400 "Paul D. Hanna" <pauldhanna at juno.com>
writes:
The question that came to mind was: "when is A111075(n) odd?"
This gives a new sequence:
"n for which  A111075(n) is odd"
1,3,4,6,12,16,24,25,27,48,49,54,64,75,96,100,108,121,147,
150,169,192,196,216,243,256,289,294,300,361,363,384,400,432,
484,486,507,529,588,600,625,675,676,726,768,784,841,864,867,
961,972,1014,1024,1083,1156,1176,1200,1225,1323,1350,1369,

Conjecture: A111075(n) is odd whenever: 
(i)  n = m^2 for all m>=1 such that 3 does not divide m, and 
(ii)  n = 3*A028982(m) for all m>=1.
Note that A028982 lists positive integers having an odd sum of divisors.
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