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 2005-11-16, 15:28 #1 Crook     Nov 2004 24 Posts Relation between divisor functions Does anybody know anything about the relation between sigma(n) and d(n) and about sigma(n)/d(n)?
2005-11-16, 15:30   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

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.

 2005-11-16, 15:34 #3 Crook     Nov 2004 24 Posts And what is the relation between these 2 functions? Last fiddled with by Crook on 2005-11-16 at 15:34
2005-11-16, 15:40   #4
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by Crook And what is the relation between these 2 functions?

Are you looking for the normal order, or the average order?

 2005-11-16, 15:42 #5 Crook     Nov 2004 24 Posts 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.
2005-11-16, 15:58   #6
R.D. Silverman

Nov 2003

746010 Posts

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

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