A note on the $\Sopfr(n)$ function

preprint2011arXivOpen access

The $\Sopfr(n)$ function is defined as the sum of prime factors of $n$ each of which is taken with its multiplicity. This function is studied numerically. The analogy between $\Sopfr(n)$ and the primes distribution function is drawn and some conjectures for prime numbers formulated in terms of the $\Sopfr(n)$ function are suggested.

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A note on the $\Sopfr(n)$ function

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