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1h
comment If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
The observation that analytic density ==> logarithmic density appears (but is not emphasized) in the proof of Theorem 1 of this 1936 paper of Erdos and Davenport: renyi.hu/~p_erdos/1936-04.pdf. They cite a 1914 theorem of Hardy and Littlewood.
16h
comment If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
OK, I went ahead and updated the answer.
16h
revised If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
added reference to Landau
1d
comment If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
You want p. 225 in the 1st edition, and p. 236 in the 2nd.
1d
answered If the natural density (relative to the primes) exists, then the Dirichlet density also exists, and the two are equal
Feb
5
answered Asymptotics of product of Euler's totient function (A001088)?
Feb
4
awarded  Enlightened
Feb
4
awarded  Nice Answer
Feb
4
answered Does the sum $\sum_{n=1}^{\infty}\frac{1}{p_n(p_{n+1}-p_n)}$ converge?
Feb
4
comment Elementary prime-generating sequences
Have you seen this paper? Shapiro, Harold N.; Sparer, Gerson H. Composite values of exponential and related sequences. Comm. Pure Appl. Math. 25 (1972), 569–615.
Feb
4
comment Does the sum $\sum_{n=1}^{\infty}\frac{1}{p_n(p_{n+1}-p_n)}$ converge?
The convergence of your series follows from upper bound sieve estimates. In fact, a somewhat stronger result is shown in this paper: Erdös, Paul(H-AOS); Nathanson, Melvyn B.(1-CUNY7) On the sum of the reciprocals of the differences between consecutive primes. Number theory (New York, 1991–1995), 97–101, Springer, New York, 1996.
Dec
19
comment If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ squarefree?
Yes, that's clearer. I've made the edit.Thanks!
Dec
19
revised If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ squarefree?
Edited as per Lucia's suggestion.
Dec
18
answered If $N = {q^k}{n^2}$ is an odd perfect number given in Eulerian form, is $n$ squarefree?
Dec
9
comment What is wrong with this counterexample to the Weak Bunyakovsky's conjecture and reformulation of Bunyakovsky's conjecture?
I do not understand the comment: "searching the web, couldn't find out how to contact the author of the paper". If you delete the last part of your URL, you are led directly to the author's website, which lists his email address.
Dec
1
awarded  Nice Answer
Dec
1
answered Are there other integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$ and $(0, -1)$?
Dec
1
comment Are there other integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$ and $(0, -1)$?
Following up on Jeremy's comment, see the answers to mathoverflow.net/questions/115063/solved-cubic-thue-equation
Nov
18
comment Proving Legendre's Sum of 3 Squares Theorem via Geometry of Numbers
Have you seen this recent arXiv preprint? arxiv.org/abs/1509.02590
Nov
8
comment What is the asymptotic growth rate of the product of divisor function up to n
Well, $f(n)=\log\tau(n)$ is an additive function; that is, $f(n) = \sum_{p^k\parallel n} f(p^k)$. Now insert this expression for $f$ into $\sum_{n \le x}f(n)$ and reverse the order of summation. I believe in this example, one finds that the main term in the asymptotic is $x \sum_{p \le x} f(p)/p$, and this is $\sim (\log 2) x\log\log{x}$, as $x\to \infty$ (Alternatively, note that $\tau(n)$ is between $2^{\omega(n)}$ and $2^{\Omega(n)}$, and use the known results --- as found in Hardy and Wright, for example --- on the partial sums of $\omega$ and $\Omega$.)