is the sum of divisors function

Euler’s totient function is the number of positive integers not exceeding that have no common divisors with (other than the common divisor 1).

In other words, is the number of integers coprime to such that

Product =

I’ll start with the Squarefree semiprimes.

Squarefree semiprimes are numbers such that

These results show a pattern.

Prove that a positive integer is the product of two primes differing by **2** iff

Also, prove that a positive integer is the product of two primes differing by **4** iff

and a positive integer is the product of two primes differing by **6** iff

and a positive integer is the product of two primes differing by **8** iff

and a positive integer is the product of two primes differing by **10** iff

and a positive integer is the product of two primes differing by **12** iff

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## About benvitalis

math grad - Interest: Number theory