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 Mar 25 awarded Yearling Apr 22 awarded Enthusiast Apr 21 answered Are sets with similar asymptotic behavior as the primes necessarily finite additive bases? Apr 17 comment Limit of $\frac{1}{n}\sum_{r=1}^n\frac{n\ (\mathrm{mod}\ r)}{r}$ To add to Emil's nice answer: The determination of the OP's limit is implicit in Dirichlet's estimate for the average order of the divisor function, namely $\sum_{k=1}^{n} d(k) = n \log{n} + (2\gamma-1)n + O(\sqrt{n})$. (See section 18.2 in Hardy and Wright, for example.) To see the connection, notice that the sum in question is exactly the number of ordered pairs of natural numbers $(r,s)$ with $rs \leq n$ (and now compare with Emil's answer above). Apr 7 answered The sum of multiplicative inverses of odd numbers Apr 5 answered Finite sums of prime numbers $\geq x$ Apr 4 comment Finite sums of prime numbers $\geq x$ Lemma 1 of Erdos's 1974 paper with Benkoski "On weird and pseudoperfect numbers" is: There is an absolute constant $c$ such that every integer $m > c p_k$ is the distinct sum of primes not less than $p_k$. (Here $p_k$ is the $k$th prime, in the usual order.) No proof is given. "The lemma is probably well known and, in any case, easily follows by Brun's method." Mar 28 comment Binary representation of powers of 3 Alternatively, one can shorten the analysis using the following theorem of Bang: $2^n-1$ has a primitive prime divisor except for $n=1$ and $n=6$. Mar 24 awarded Editor Mar 24 revised Primes $1 + x^2 + y^2$ added 103 characters in body Mar 24 awarded Teacher Mar 24 answered Primes $1 + x^2 + y^2$