duplicate hunting, pt. 14

[Andrew Plewe]

On 5/10/07, Andrew Plewe <aplewe at sbcglobal.net> wrote:
> A067139 and A078645
> http://www.research.att.com/~njas/sequences/?q=id:A067139|id:A078645

If I understand the definitions, then these sequences are identical.

> A088669 and A091580
> http://www.research.att.com/~njas/sequences/?q=id:A088669|id:A091580

No, these differ.  A088669(121) is one less than A091580(121), and
thereafter the difference steadily increases.

> A072061 and A095721 (possibility noted in comments to A095721)
> http://www.research.att.com/~njas/sequences/?q=id:A072061|id:A095721

I'm pretty sure these are the same, but less sure than I was about the
other pairs.  I think someone else should look.

> A034287 and A067128 (possibility noted in comments to A067128)
> http://www.research.att.com/~njas/sequences/?q=id:A034287|id:A067128

Hm, the question is if there's a number that sets a new record for
product of divisors without at least tying for number of divisors, or
conversely if it at least ties the record for number of divisors
without setting a record for product.

I don't know enough off the top of my head to prove it.  But rather
than checking up to 1.5 million as mentioned in that comment, you
could generate a nice big b-file for the Ramanujan sequence from the
lists of prime exponents (they rounded the numbers, so we'd need to do
some multiplying):
  http://wwwhomes.uni-bielefeld.de/achim/highly.html
and then we just need similarly many terms for the "largest product of
divisors" sequence and we can at least see if there are any "small"
exceptions.

--Joshua Zucker