Re: [math-fun] what is known about the squareful Fibonacci numbers?
So I'm guessing we have at least three sequences under discussion (or at least confusion): "Squareful numbers are numbers for which at least one prime factor exponent is [exactly] 2" which gives A038109: 4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, ... "squarefull numbers [are] numbers for which each prime factor exponent is at least 2" which gives A001694: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, ... Mike Speciner's "at least one prime factor exponent is at least 2" which gives A013929: 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, ... On 7/16/12, Mike Speciner <ms@alum.mit.edu> wrote:
Under that definition, 8 would not be squareful. From the example in the referenced webpage, I would guess it's supposed to say "at least one prime factor exponent is at least 2"
On 7/16/2012 9:37 AM, Wouter Meeussen wrote:
http://oeis.org/wiki/Squareful_numbers
"Squareful numbers are numbers for which at least one prime factor exponent is 2, thus are not squarefree numbers, not to be confused with squarefull numbers, numbers for which each prime factor exponent is at least 2. "
-----Original Message----- From: Robert Munafo Richard Guy probably uses "UPINT" [to refer] to "Unsolved Problems In Number Theory", a book that perhaps defines "powerful number" in a similar way to the following:
An integer m such that if p | m, then p^2 | m, is called a powerful number.
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
I'm getting caught up on emails from the part month. About "squarefull" numbers: I think the official version is A001694, and A013929 and A038109 should not have squarefull as part of their primary definition (but only mentioned as alternative, deprecated, names in the Comments) I've made appropriate changes to the three entries and I've updated the entry in the Index. It is clearly a bad idea to use the number of l's at the end of squarefull to distinguish the different versions, since both spellings seem to be in current use (and I'm not sure which spelling is more correct!). Neil On Mon, Jul 16, 2012 at 4:26 PM, Robert Munafo <mrob27@gmail.com> wrote:
So I'm guessing we have at least three sequences under discussion (or at least confusion):
"Squareful numbers are numbers for which at least one prime factor exponent is [exactly] 2" which gives A038109: 4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, ...
"squarefull numbers [are] numbers for which each prime factor exponent is at least 2" which gives A001694: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, ...
Mike Speciner's "at least one prime factor exponent is at least 2" which gives A013929: 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, ...
On 7/16/12, Mike Speciner <ms@alum.mit.edu> wrote:
Under that definition, 8 would not be squareful. From the example in the referenced webpage, I would guess it's supposed to say "at least one prime factor exponent is at least 2"
On 7/16/2012 9:37 AM, Wouter Meeussen wrote:
http://oeis.org/wiki/Squareful_numbers
"Squareful numbers are numbers for which at least one prime factor exponent is 2, thus are not squarefree numbers, not to be confused with squarefull numbers, numbers for which each prime factor exponent is at least 2. "
-----Original Message----- From: Robert Munafo Richard Guy probably uses "UPINT" [to refer] to "Unsolved Problems In Number Theory", a book that perhaps defines "powerful number" in a similar way to the following:
An integer m such that if p | m, then p^2 | m, is called a powerful number.
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
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