There are infinitely many solutions to the equation for so this value is excluded in the definition.
[1] The concept is somewhat analogous to that of highly composite numbers.
Just as there are infinitely many highly composite numbers, there are also infinitely many highly cototient numbers.
, i.e. the number of positive integers less than or equal to
For example, the cototient of 6 is 4 since these four positive integers have a prime factor in common with 6: 2, 3, 4, 6.
(sequence A063740 in the OEIS) The first few highly cototient numbers which are primes are [2]