[seqfan] A180710 Sum of Divisors of 2^(n-1)*a(n-1)

Paul D Hanna pauldhanna at juno.com
Mon Oct 8 04:23:57 CEST 2012


SeqFans, 
      Consider the conjecture stated in  http://oeis.org/A180710 : 
 
Given  a(n) = sigma( 2^(n-1)*a(n-1) )   for n>1 with a(1)=1, 
then    sigma(n) | a(n)   for n>=1.  
 
The conjecture holds for at least the first 45 terms.  
 
Can someone provide a proof / argument / counter-example for this conjecture? 
  
If we instead set  a(n) = sigma( 3^(n-1)*a(n-1) ) : 
[1, 4, 91, 4480, 1481040, 1460531520, 4837816811520, 49012450341076992, 1372628133681007230720, ...] 
then no similiar pattern seems to hold. 
 
Thanks, 
     Paul 




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