Arithmetic Functions II

The deeper problems associated with some arithmetic functions, such as the gap problem of squarefree numbers, are consider. Such items include also moment sums, and the notion of normal order. The Hardy–Ramanujan theorem on the normal order of the prime divisor function is given, and there is a proof of Segal’s that Euler’s totient function does not have a normal order. There are descriptions of highly composite numbers and sparsely totient numbers.