Monotonic Divergent Series of Number Theoretic Functions

List of monotonic divergent series involving the following number theoretic functions:

$\sigma_0(n)$ denotes the count of divisors of the natural number $n$ .

$\sigma_1(n)$ denotes the sum of divisors of the natural number $n$ .

$\Omega(n)$ denotes the count of prime divisors of the natural number $n$ .

$\omega(n)$ denotes the count of distinct prime divisors of the natural number $n$ .

$\varphi(n)$ denotes Euler’s totient function of the natural number $n$ .

GENERA

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