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Talk:P-rough numbers

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1 as a p-rough number?!

The OEIS considers 1 as a -rough number for any , although it doesn't have a smallest prime factor. — Daniel Forgues 05:47, 6 September 2012 (UTC)

Yes, all of its prime factors are p or greater. The least prime factor definition is equivalent for numbers other than 1. Similarly, for p-smooth numbers the true definition is "all prime factors are at most p" so as to exclude 0, even though the definition "gpf(n) <= p" is otherwise equivalent. Charles R Greathouse IV 04:36, 7 September 2012 (UTC)
In a strict sense, 1 (having no prime factors) should not be included among the p-smooth numbers or p-rough numbers. The only numbers which are p-smooth numbers and p-rough numbers are prime powers p^n (I guess by letting n = 0, this could justify 1 being a p-smooth number and p-rough number for any p). — Daniel Forgues 05:07, 7 September 2012 (UTC)