An Arithmetic Function Arising from the Dedekind Ψ Function

  title={An Arithmetic Function Arising from the Dedekind Ψ Function},
  author={Colin Defant},
We define ψ to be the multiplicative arithmetic function that satisfies ψ(p) = { pα−1(p+ 1), if p 6= 2; pα−1, if p = 2 for all primes p and positive integers α. Let λ(n) be the number of iterations of the function ψ needed for n to reach 2. It follows from a theorem due to White that λ is additive. Following Shapiro’s work on the iterated φ function, we determine bounds for λ. We also use the function λ to partition the set of positive integers into three sets S1, S2, S3 and determine some… CONTINUE READING

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Showing 1-6 of 6 references

An arithmetic function arising from the φ function

  • H. Shapiro
  • Amer. Math. Monthly 50
  • 1943
Highly Influential
6 Excerpts

Iterations of generalized Euler functions

  • G. K. White
  • Pacific J. Math. 12 (1962) 777–783. Colin Defant…
  • 2015
2 Excerpts

Representing and counting the subgroups of the group Zm × Zn

  • M. Hampejs, N. Holighaus, L. Tóth, C Wiesmeyr
  • Journal of Numbers
  • 2014
1 Excerpt

, A generalization of Sylvester ’ s and Frobenius ’ problems on numerical semigroups

  • Zdzis law Skupień
  • Acta Arith
  • 1971

Introduction to the arithmetic theory of automorphic functions

  • Goro Shimura
  • Amer . Math . Monthly
  • 1971
1 Excerpt

Concerning the iterated φ function

  • P. A. Catlin
  • Amer. Math. Monthly 77
  • 1970
1 Excerpt

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