Minima of Phi(m) over m
- From: Jean-Claude Evard <Jean-Claude.Evard@xxxxxxx>
- Date: Wed, 29 Jun 2005 14:30:06 +0000 (UTC)
Is it already known that over an interval of integers
[2, N], the ratio Phi(m) over m is minimum when m
is the largest primorial that lies in this interval ?
Here:
Phi(m) = Euler`s function
= Number of integers k
such that 0<k<m and gcd(k,m)=1.
primorial = product of the smallest primes:
2# = 2 primorial = 2,
3# = 3 primorial = 2*3 = 6,
5# = 5 primorial = 2*3*5 = 30,
7# = 7 primorial = 2*3*5*7 = 210,
.........
With many thanks for your time and attention,
Jean-Claude Evard
Department of Mathematics
Western Kentucky University
.
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