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.
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