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Message from discussion Reciprocals of integers summing to 1

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More options Nov 18 2012, 7:45 am
Newsgroups: sci.math
From: Bill Taylor <wfc.tay...@gmail.com>
Date: Sun, 18 Nov 2012 04:45:04 -0800 (PST)
Local: Sun, Nov 18 2012 7:45 am
Subject: Re: Reciprocals of integers summing to 1
Quite clearly a lot of respondents didn't seem to read the question!

> For each n, what are the solutions in positive integers
> to (1/X1)+(1/X2) + . . . + (1/Xn)=1 ?

but in such contexts they are almost always regarded as the same.

Clearly repeats among the x_i are allowed.
(Though one could also answer with them disallowed.)

But most important, A FUNCTION OF  n  IS REQUIRED.

i.e.  what is  f(n) = card({x1, x2, ... , xn} | etc)

where the curly brackets denote unordered multisets.

So far we have  f(1) = 1,  f(2) = 1, f(3) = 3 (seemingly)
and no great effort on any higher values.

If no-one can get anywhere much theoretically,
can some computer whizz at least produce a list of
the first several values of  f  please?

-- Whacking Willy.

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