Seq A119428: Records Table

[Paul D. Hanna]

Seqfans,
      Consider A119428, the Moebius transform of the 
period 10 sequence: [1,1,1,1,0,-1,-1,-1,-1,0] (with offset 1). 
Using PARI, n>=1: 
a(n)=sumdiv(n,d,[1,1,1,1,0,-1,-1,-1,-1,0][(d-1)%10+1]). 
 
I am interested in the record values of this sequence. 
So far it seems that the record values form A003586, 
the 3-smooth numbers of the form 2^k*3^n for k,n >=0. 
Can anyone prove this? 
 
Now the positions at which these numbers first occur 
in A119428 are also intriguing. 
 
Here is what I was able to find so far:
 
1:1, 2:2, 12:4, 132:8, 4092:16, 167772:32, ...
4:3, 44:6, 924:12, 28644:24, 1174404:48, ...
484:9, 10164:18, 315084:36, ...
465124:27, ...
...
The above format is "m:A119428(m)," position m followed by term, and 
placed in the table in row n and column k when 3^n*2^k = A119428(m). 
  
Is there a formula for the position where 3^n*2^k first occurs in A119428
?
 
Note that the positions of the powers of 3 seem to be all squares:  
[1, 4, 484, 465124,...]  = [1, 2^2, 22^2, 682^2, ...]. 
Do the positions where 3^n first occurs in A119428 continue to be
squares?  
 
Answering these questions may be a hard computational task, 
but if someone extended the table a bit, it would give more insight. 
 
Or, can anyone provide number theory that would apply and simplify? 
 
Thanks,
     Paul
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