User a_mse_user - MathOverflowmost recent 30 from http://mathoverflow.net2013-06-19T15:27:16Zhttp://mathoverflow.net/feeds/user/15702http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/67436/is-there-any-sequence-a-n-of-nonnegative-numbers-for-which-sum-n-geq-1a-nIs 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_user2011-06-10T12:31:12Z2012-01-13T07:07:57Z
<p>Is there any sequence $a_n$ of nonnegative numbers for which $\displaystyle\sum_{n \geq 1}a_n^2 <\infty$ 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-algorithmPrime generating algorithma_MSE_user2011-09-29T13:17:42Z2011-09-29T13:27:48Z
<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>