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Old 2005-11-16, 15:28   #1
Crook
 
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Default Relation between divisor functions

Does anybody know anything about the relation between sigma(n) and d(n) and about sigma(n)/d(n)?
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Old 2005-11-16, 15:30   #2
R.D. Silverman
 
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Quote:
Originally Posted by Crook
Does anybody know anything about the relation between sigma(n) and d(n) and about sigma(n)/d(n)?
Yes.
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Old 2005-11-16, 15:34   #3
Crook
 
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And what is the relation between these 2 functions?

Last fiddled with by Crook on 2005-11-16 at 15:34
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Old 2005-11-16, 15:40   #4
R.D. Silverman
 
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Quote:
Originally Posted by Crook
And what is the relation between these 2 functions?
You didn't ask that question!!


Are you looking for the normal order, or the average order?
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Old 2005-11-16, 15:42   #5
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I thought the question was clear enough. I'm asking some general informations about the relation between these 2 functions. For instance, sigma(n)/d(n). I'd be interested in both the average order and the normal order.
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Old 2005-11-16, 15:58   #6
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Quote:
Originally Posted by Crook
I thought the question was clear enough. I'm asking some general informations about the relation between these 2 functions. For instance, sigma(n)/d(n). I'd be interested in both the average order and the normal order.

The normal order doesn't exist for d(n). This is what makes your
question less than trivial. Hardy & Wright has an excellent discussion
of your questions.
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