Date: Nov 23, 2012 7:16 AM
Author: Bill Taylor
Subject: Re: Reciprocals of integers summing to 1
On Nov 23, 3:08 pm, david petry <david_lawrence_pe...@yahoo.com>

wrote:

> On Thursday, November 22, 2012 4:07:09 AM UTC-8, Bill Taylor wrote:

>

> > If anyone wants to check my hand work, the number

> > of ways of splitting 1/m is (I suggest)

>

> > m: 1 2 3 4 5 6 7 8 9 10 12 15 18 20 24 42

> > #(m) 1 2 2 3 2 5 2 4 3 5 4 5 8 8 11 14

>

> > It seems that #(p) = 2 for prime p, and in general

In fact this is simply routinely proved, unsurprisingly.

> > the # function bears a close resemblance to d, the number

> > of factors of m; though it tends to be a bit bigger,

> > and is not multiplicative like d.

>

> The formula 1/(a*b) = 1/(a*(a+b)) + 1/(b*(a+b)) shows why

> there is a close relation between your function and

> the number of ways the number can be factored into two factors.

Of course! Neat triviality. I wonder if the surplus ways

are also simply characterizable. Must investigate.

-- Bumbling Bill

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