Is it true that for all positive integers n, the inequality holds?
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Originally Posted by alexmahone Is it true that for all positive integers n, the inequality holds? I assume from the title that is the number of divisors of . Does that hold for
Originally Posted by Plato I assume from the title that is the number of divisors of . Does that hold for 144 = 12^2 d(144) = 2 + 1 = 3 It does hold for n = 144.
Uh... no! 1 2 3 4 6 8 9 12 16 ... all divide 144, so the left hand side is larger than the right hand side
Originally Posted by TheChaz Uh... no! 1 2 3 4 6 8 9 12 16 ... all divide 144, so the left hand side is larger than the right hand side Oops ... I should have done: 144 = 2^4 * 3^2 d(n) = (4 + 1)(2 + 1) = 15
Originally Posted by alexmahone 144 = 12^2 d(144) = 2 + 1 = 3 It does hold for n = 144. Because then .
Perhaps there is a mistake in the book: Is true?
Originally Posted by alexmahone Perhaps there is a mistake in the book: Is true? The divisor bound « What’s new
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