In number theory, a branch of mathematics, a highly cototient number is a positive integer <math>k</math> which is above 1 and has more solutions to the equation
:<math>x - \phi(x) = k</math>
than any other integer below <math>k</math> and above 1. Here, <math>\phi</math> is Euler's totient function. There are infinitely many solutions to the equation for
:<math>k</math> = 1
so this value is excluded in the definition. The first few highly cototient numbers are:
:2, 4, 8, 23, 35, 47, 59, 63, 83, 89, 113, 119, 167, 209, 269, 299, 329, 389, 419, 509, 629, 659, 779, 839, 1049, 1169, 1259, 1469, 1649, 1679, 1889, ...
Many of the highly cototient numbers are odd.
:2, 23, 47, 59, 83, 89, 113, 167, 269, 389, 419, 509, 659, 839, 1049, 1259, 1889, 2099, 2309, 2729, 3359, 3989, 4289, 4409, 5879, 6089, 6719, 9029, 9239, ...
See also
- Highly totient number