Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Reciprocals of integers summing to 1
Replies: 21   Last Post: Nov 23, 2012 8:44 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Bill Taylor

Posts: 186
Registered: 11/17/10
Re: Reciprocals of integers summing to 1
Posted: Nov 23, 2012 7:16 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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

** There is no moral right to "not be offended".
** There should be no legal right to "not be offended" !



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.