In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function, has no solution for . The cototient of is defined as , so a noncototient is a number that is never a cototient.
In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function, has no solution for . The cototient of is defined as , so a noncototient is a number that is never a cototient.
It is conjectured that all noncototients are even. This follows from a modified form of the slightly stronger version of the Goldbach conjecture: if the even number can be represented as a sum of two distinct primes and , then
Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).