[seqfan] Fwd: A conjecture of yours

franktaw at netscape.net franktaw at netscape.net
Sun Dec 11 19:14:02 CET 2011

I attempted to send the email below. It bounced, with the following 

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Any help would be appreciated.

Franklin T. Adams-Watters

-----Original Message-----
From: franktaw <franktaw at netscape.net>
To: J.R.Britnell <J.R.Britnell at bristol.ac.uk>
Sent: Sun, Dec 11, 2011 11:58 am
Subject: Re: A conjecture of yours

Dear John,

Thanks for the note. I don't specifically remember making this
conjecture, but I think I can answer your questions anyhow.

1. I certainly do not know of any proof.
2. It may have appeared in the seqfan mailing list;  I can't be sure. I
would consider the OEIS entry to be the primary publication of the
3. The numerical evidence was the main thing. Besides that, I probably
had an intuitive feeling that these were similar things. Certainly
nothing more than that.

I'm always happy to have someone prove one of my conjectures.

Franklin T. Adams-Watters

-----Original Message-----
From: JR Britnell <J.R.Britnell at bristol.ac.uk>

Dear Franklin,

I'm trying to follow up a reference to you on the Online Encyclopedia
Integer Sequences. Apparently you conjectured in 2006 that the
sequences are equal:

A061256   Euler transform of sigma(n),
A079860   number of commuting triples from Sym(n), divided by n!.

Your conjecture is correct. I have a fairly short proof of it, which I'm
thinking of writing up.

Can you help me with any of the following information?
1. Do you know of a proof already, either published or unpublished?
2. For citation purposes, did your conjecture appear anywhere before
3. What led to your conjecture? Was there anything beyond the numerical

I'd be very grateful for your help.

Best wishes,
John Britnell

John R Britnell
Heilbronn Research Fellow
University of Bristol
J.R.Britnell at bristol.ac.uk


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