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In number theory, a branch of mathematics, a highly cototient number is a positive integer k {\displaystyle k} which is above 1 and has more solutions to the equation
than any other integer below k {\displaystyle k} and above 1. Here, ϕ {\displaystyle \phi } is Euler's totient function. There are infinitely many solutions to the equation for
so this value is excluded in the definition. The first few highly cototient numbers are:
Many of the highly cototient numbers are odd. In fact, after 8, all the numbers listed above are odd, and after 167 all the numbers listed above are congruent to 29 modulo 30.
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