# [seqfan] Re: What is a "Q unit fraction"?

Allan Wechsler acwacw at gmail.com
Sun Dec 23 00:43:31 CET 2018

```If Q is a number that depends on n in some way, we are already in trouble
for a(1). We are told a(1) = 2. That means that there are 2 ways to write
1/1 as the sum of Q unit fractions.

Unfortunately, 2 does not occur in the sequence A002966, the number of ways
to write 1 as the sum of n reciprocals.

So I am guessing that "Q unit fractions" must be a term of art, but I can't
guess what it means.

On Sat, Dec 22, 2018 at 3:18 PM Neil Sloane <njasloane at gmail.com> wrote:

> I will ask Bob Wilson directly
>
> In the mean time I added "obsc" (to A016013).
>
> Q is pretty certainly a numerical value (or range), since A016017 is
> %N A016017 Smallest k such that 1/k can be written as a sum of exactly 2
> unit fractions in n ways.
> and - also from Bob Wilson  - there is:
> %N A018892 Number of ways to write 1/n as a sum of exactly 2 unit
> fractions.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Email: njasloane at gmail.com
>
>
>
> On Sat, Dec 22, 2018 at 2:46 PM Alex Meiburg <timeroot.alex at gmail.com>
> wrote:
>
> > Two guesses. First option: this is a "q-analog" of a unit fraction. There
> > are "q-analogs" of a variety of quantities, but I don't understand them
> > very well and I think you'd have to specify q? Maybe it ends up being
> > independent of q here, though.
> >
> > Second option: you're misparsing the description, and instead of
> > decomposing into "Q unit fractions", it's decomposing into plain old unit
> > fractions, of which there are Q. Q is some variable that hasn't been
> > properly explained.
> >
> > Actually, I'd bet on the second one, given that they say "exactly Q" unit
> > fractions, which really suggests that Q is a quantity of unit fractions.
> >
> > On Sat, Dec 22, 2018, 11:30 AM Sean A. Irvine <sairvin at gmail.com wrote:
> >
> > > A016013 Number of ways to write 1/n as a sum of exactly Q unit
> fractions.
> > >
> > > Not a lot of information to go on here.
> > >
> > > Sean.
> > >
> > > --
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> > >
> >
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> >
>
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>

```