[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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