Problem 70: Totient permutation
Euler's Totient function, φ(n
) [sometimes called the phi function], is used
to determine the number of positive numbers less than or equal to n
which are
relatively prime to n
. For example, as 1, 2, 4, 5, 7, and 8, are all less than
nine and relatively prime to nine, φ(9)=6. The number 1 is considered to be
relatively prime to every positive number, so φ(1)=1.
Interestingly, φ(87109)=79180, and it can be seen that 87109 is a permutation of 79180.
Find the value of n
, 1 < n
< 107, for which φ(n
) is a permutation of n
and the ratio n
/φ(n
) produces a minimum.
Test
{{test}}Console output