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1991•Glasgow Mathematical JournalOpen access

On sparsely totient numbers

Glyn Harman

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Abstract

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

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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

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Available abstract

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

Key concepts: Euler's totient function, Multiplicative function, Mathematics, Combinatorics, Prime (order theory), Prime factor, Discrete mathematics, Euler's formula

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