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. " Elsewhere on the web, the descriptor "square-full" (with - dash) is used, probably in accordance with orthography. Apologies for the confusion, Wouter. -----Original Message----- From: Robert Munafo Sent: Monday, July 16, 2012 5:58 AM To: math-fun Cc: mbgreen@cis.upenn.edu ; greenwald@cis.upenn.edu Subject: Re: [math-fun] what is known about the squareful Fibonacci numbers? Richard Guy probably uses "UPINT" refers 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. (which is from http://mathworld.wolfram.com/PowerfulNumber.html ) So the "confusion" would be if some folks thought that only powerful numbers can be "squareful", e.g. 144 could be "squareful" but 2584 would not be because it has 17 as a factor but not 17^2. On 7/15/12, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
Dear all, I fear that there is confusion about the definition of ``squareful''. See section on powerful numbers in UPINT. R.
-- 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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun