Values taken many times by Euler's phi-function

Author:
Kent Wooldridge

Journal:
Proc. Amer. Math. Soc. **76** (1979), 229-234

MSC:
Primary 10A20; Secondary 10H30

DOI:
https://doi.org/10.1090/S0002-9939-1979-0537079-1

MathSciNet review:
537079

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Abstract: Let denote the number of integers *n* such that , where is Euler's function. Erdős has proved that there is a such that for infinitely many *m*. In this paper we show that we may take to be any number less than .

**[1]**P. Erdős,*On the normal number of prime factors of**and some related problems concerning Euler's*-*function*, Quart. J. Math. Oxford Ser.**6**(1935), 205-213.**[2]**H. Halberstam and H.-E. Richert,*Sieve methods*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], London-New York, 1974. London Mathematical Society Monographs, No. 4. MR**0424730****[3]**D. G. Kendall and R. A. Rankin,*On the number of Abelian groups of a given order*, Quart. J. Math., Oxford Ser.**18**(1947), 197–208. MR**0022569**

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0537079-1

Article copyright:
© Copyright 1979
American Mathematical Society