[seqfan] Re: More (composite) terms for A233281

David Applegate david at research.att.com
Mon Feb 10 22:14:53 CET 2014


> There appear to be an Eulerian number < http://oeis.org/A000295 > of solutions in each case.

Every squarefree number has an Eulearian number of composite divisors
(if a number is the product of n distinct primes, then it has 2^n-n-1
composite divisors).

Nobody has found a prime index Fibonacci numbers that isn't
squarefree, but on the other hand, nobody has proved that they're all
squarefree, either.

-Dave

> From seqfan-bounces at list.seqfan.eu Mon Feb 10 12:13:00 2014
> From: Hans Havermann <gladhobo at teksavvy.com>
> Date: Mon, 10 Feb 2014 12:12:43 -0500
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: More (composite) terms for A233281

> Attempting to understand this sequence better I have just posted a (hopefully) complete list of composites derived from Fibonacci numbers with prime indices, up to index 997:

> http://chesswanks.com/num/CompositeDivisorsOfPrimeIndexFibonaccis.txt

> There appear to be an Eulerian number < http://oeis.org/A000295 > of solutions in each case. Antti's composites will of course be the sorted collection of all these solutions to infinity. My question is still how one might know that smallish solutions (say, up to a given size) will not come from unsolved, future Fibonaccis.

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