User a_mse_user - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T15:27:16Z http://mathoverflow.net/feeds/user/15702 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/67436/is-there-any-sequence-a-n-of-nonnegative-numbers-for-which-sum-n-geq-1a-n Is there any sequence $a_n$ of nonnegative numbers for which $\sum_{n \geq 1}a_n^2 <\infty$ and $\sum_{n \geq 1}\left(\sum_{k \geq 1}\frac{a_{kn}}{k}\right)^2=\infty$? a_MSE_user 2011-06-10T12:31:12Z 2012-01-13T07:07:57Z <p>Is there any sequence $a_n$ of nonnegative numbers for which $\displaystyle\sum_{n \geq 1}a_n^2 &lt;\infty$ and</p> <p>$$\sum_{n \geq 1}\left(\sum_{k \geq 1}\frac{a_{kn}}{k}\right)^2=\infty\quad?$$</p> <p>See also <a href="http://math.stackexchange.com/questions/42624/double-sum-miklos-schweitzer-2010" rel="nofollow">http://math.stackexchange.com/questions/42624/double-sum-miklos-schweitzer-2010</a></p> http://mathoverflow.net/questions/76761/prime-generating-algorithm Prime generating algorithm a_MSE_user 2011-09-29T13:17:42Z 2011-09-29T13:27:48Z <p>If I want an algorithm that outputs <em>any</em> $n$ distinct prime numbers, is there anything faster than Atkins' Sieve $O(n/log(log(n))$ ?</p>