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Sparsely totient number

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In mathematics, a sparsely totient number is a certain kind of even natural number. A natural number, n, is sparsely totient if for any m > n,

φ(m)>φ(n),

where φ is Euler's totient function. The first few sparsely totient numbers are:

2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630.

These are listed in (sequence A036913 in the OEIS).

References

  • Roger C. Baker & Glyn Harman, "Sparsely totient numbers," Annales de la faculte des sciences de Toulouse Ser. 6 5 no. 2 (1996): 183 - 190
  • D. W. Masser & P. Shiu, "On sparsely totient numbers," Pacific J. Math. 121, no. 2 (1986): 407 - 426.
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