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Published online by Cambridge University Press: 18 May 2009
Following Masser and Shiu [6] we say that a positive integer n is sparsely totient if

Here φ is the familiar Euler totient function. We write ℱ for the set of sparsely totient numbers. In [6] several results are proved about the multiplicative structure of ℱ. If we write P(n) for the largest prime factor of n then it was shown (Theorem 2 of [6]) that

and infinitely often
