Talk:Square-free integer

message: I know, but here's another:The number of divisors of a squarefree integer is a power of two.Rich 06:55, 1 November 2006 (UTC)
replies: text: How about 8? Its 4=2^2 factors are 1, 2, 4 and 8, but it is not square-free. 128.101.10.146 23:22, 7 June 2007 (UTC)
replies: text: Indeed. Having a number of divisors that is a power of two is a necessary, but not sufficient, condition for being squarefree. Doctormatt 23:39, 7 June 2007 (UTC)
thread_title:  We have a lot of equivalent characterizations already, 

message: Is it known something about the complexity of testing if an integer is square-free? Maybe some relation with Primality test. 193.144.198.250 (talk) 11:28, 11 March 2014 (UTC)
thread_title:  Square-free test 

message: I cannot understand: whether today any mathematicians consider squarefree numbers without 1 or not. Is it possible (for contemporary scientists) to define "squarefree number" as "a number that is the product of integer number of different primes"? --Tamtam90 (talk) 22:06, 5 August 2017 (UTC)
replies: text: Square free numbers may be defined as products of primes that are all different. This definition is equivalent with the one that is given in the first sentence of the article, as 1 is the empty product of primes. Thus, presently, 1 is always defined to be square free. D.Lazard (talk) 08:30, 6 August 2017 (UTC)
replies: text:  Thank you for your answer. I think I'd ask about this subject Mr. John Derbyshire and Mr. Dennis Hejhal. --Tamtam90 (talk) 23:57, 7 August 2017 (UTC)
thread_title:  1 as a squarefree integer 

message: This business about having two completely different definitions for « squarefull » and « squareful » (according to the number of « l » of the word) is not confirmed by common practice in mathematical publications. A search in MathSciNet with 
"squarefull integer" or "squarefull integers", anywhere, yields 10 articles, and with "squarefull number" or "squarefull numbers", anywhere, yields 21 articles. The same searches with only one « l » in « squareful » yield 0, resp. 8 articles. In the last output the definition of « Squareful » is the same as that of « squarefull », except in one single article, in which it is indeed defined as « not squarefree » (but for which the reviewer nevertheless writes « squarefull » with two « l » in his review…). 
Now OEIS is a wiki, and provides zero source for its page ; as for the page  of Mathworld, it provides as unique reference 4 sequences from … OEIS (which in passing do not include the one on « squareful numbers », and all of which explicitly concern « non squarefree numbers » , and not « squareful numbers ») .--Sapphorain (talk) 07:01, 24 August 2020 (UTC)
replies: text:  OK, leave it out. Bubba73 You talkin' to me? 16:46, 24 August 2020 (UTC)
thread_title:  squarefull and squareful 

message: This page has been moved without discussion from  to squarefree number. The new title is confusing, as "square-free" is nonsensical when applied to numbers that are not integers. So, I'll ask to revert this move. D.Lazard (talk) 20:36, 24 September 2021 (UTC)
replies: text: I *think* I've always seen it called "number". Bubba73 You talkin' to me? 01:52, 25 September 2021 (UTC)
thread_title:  Moved without any discussion