Abstract
An asymptotic formula is given for the number of integers n≤x for which φ(n) is not divisible by a given odd prime.
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Erdős, P., Granville, A., Pomerance, C. and Spiro, C., On the normal behavior of the iterates of some arithmetic functions, in Analytic Number Theory (Allerton Park, IL, 1989), pp. 165–204, Birkhäuser, Boston, MA, 1990.
Luca, F. and Pomerance, C., On some problems of Makowski–Schinzel and Erdős concerning the arithmetical functions φ and σ, Colloq. Math.92 (2002), 111–130.
Narkiewicz, W., Elementary and Analytic Theory of Algebraic Numbers, Springer, Berlin–Heidelberg–New York, 1990.
Odoni, R. W. K., A problem of Rankin on sums of powers of cusp-form coefficients, J. London Math. Soc.44 (1991), 203–217.
Prachar, K., Primzahlverteilung, Springer, Berlin–Göttingen–Heidelberg, 1957.
Williams, K. S., Mertens’ theorem for arithmetic progressions, J. Number Theory6 (1974), 353–359.
Wirsing, E., Das asymptotische Verhalten von Summen über multiplikative Funktionen, Math. Ann.143 (1961), 75–102.
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Spearman, B., Williams, K. Values of the Euler phi function not divisible by a given odd prime. Ark Mat 44, 166–181 (2006). https://doi.org/10.1007/s11512-005-0001-6
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DOI: https://doi.org/10.1007/s11512-005-0001-6