20090418, 00:54  #1 
Dec 2008
1501_{8} Posts 
Poulet numbers with 3 distinct prime factors
I know that in 2004 Galway conjectured a formula for the Poulet number counting function with 2 distinct prime factors. I was wondering if there are any conjectures for the Poulet number (not necessarily Carmichael numbers) counting function with 3 distinct prime factors or how Galway's formula could be extended for 3 distinct prime factors?

20090418, 03:57  #2  
Dec 2008
1101000001_{2} Posts 
Quote:


20090418, 14:18  #3 
Dec 2008
7^{2}·17 Posts 
Just now I was looking at a paper of Erdos, and he states the pseudoprimes with k distinct factors are bounded by
Although these bounds are weak (and were improved by Pomerance), the upperbound looks a lot like my formula, eh? Note the trivial fact that: . 
20090419, 00:56  #4 
Dec 2008
7^{2}×17 Posts 
So does anyone have any ideas at all? It's fine if they are not good, all I just want are some responses at least (especially the experts)! C'mon guys, it's like a freaking ghost town on this thread!

20090419, 04:07  #5 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 

20090419, 04:23  #6  
Dec 2008
7^{2}·17 Posts 
Quote:
If only I had friends to hang out with on a Saturday night.... Anyways, cheesehead, do you have any ideas at all (since you were the first one who responded )? Last fiddled with by flouran on 20090419 at 04:26 Reason: I wanted to include my music preferences 

20090419, 05:21  #7  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
As for ideas about hobbies and/or friends: List your interests, then consider how meeting with other people would fit in. Two quick examples (not claimed to be representative!): Stamp collecting  There are conventions and shows. Friendmaking potential would lie in conversations one struck up before, during and after the main event. Thrash metal songs  I'm not especially familiar with this genre, but I suspect that all song genres would have in common (more or less ...) that (a) folks could get together to sing [hmm... a thrash metal choir ], (b) a small group could form a band to play the music for others to sing [but that's who you're listening to: small groups Megadeth and Metallica!], or (c) folks could get together to attend a performance. Friendmaking potential would mainly lie in conversations one struck up before and after the main event. There  now extend the list! 

20090419, 08:16  #8  
Dec 2008
7^{2}×17 Posts 
Quote:
Quote:
Just kidding. Anyways, so back on topic, anyone at all have any clues? At all? Even the slightest clue? Last fiddled with by flouran on 20090419 at 08:16 

20090419, 10:57  #9 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6456_{10} Posts 
I know that 3*5*7 = 105. Three prime factors right there. Hope that helps.
So, remind me again, what is this thread about anyway? 
20090419, 15:12  #10  
Dec 2008
7^{2}×17 Posts 
Quote:
This thread is about what the formula is which counts the number of basepseudoprimes with 3 prime factors. 

20090429, 03:57  #11  
Dec 2008
7^{2}·17 Posts 
Quote:


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