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Summing Euler’s Φ -function

Published online by Cambridge University Press:  01 August 2016

Norman Routledge
Norman Routledge*
Affiliation:
24 Rothsay Street, Bermondsey, London SE1 4UE
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Extract

Euler’s Φ(n) is the number of positive integers n with no factor in common with n. We wish to calculate

This problem arises in connection with the Farey series Fn, i.e. all the fractions from 0/1 to 1/1 (inclusive) with denominator n in their lowest terms, in order of size, so that for example

Type
Articles
Information
The Mathematical Gazette , Volume 92 , Issue 524 , July 2008 , pp. 242 - 251
Copyright
Copyright © The Mathematical Association 2008

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References

1. Neville, E. H., The Farey series of order 1025, Cambridge University Press (1950).Google Scholar
2. Hardy, G. H. and Wright, E. M., An introduction to the theory of numbers (5th edn.) Clarendon Press, Oxford (1979).Google Scholar