Timeline for Asymptotic value of sum over Möbius function
Current License: CC BY-SA 3.0
3 events
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| Apr 12, 2016 at 11:25 | comment | added | user45947 | @Lucia: Thanks! Guess I should have seen this. My motivation for asking the question is trying to understand the behaviour of the sum $\sum_{\substack{ {d\mid P(\sqrt{x}) }\\ {d\leq x} \\ {|\mathcal{A}_d(a)| = \lfloor x/d \rfloor+1 } }} \mu(d)$, described in this MO question under the heading "Legendre sieve perspective". I'm a bit stuck here and would be grateful for any suggestions on how to attack the problem. | |
| Apr 12, 2016 at 1:19 | comment | added | Lucia | You're just asking for square-free numbers below $x$ with no prime factor larger than $\sqrt{x}$. The answer is $\sim (6/\pi^2)x (1-\log 2)$, where $(6/\pi^2)$ comes from the square-free-ness, and $1-\log 2$ from having no prime factor larger than $\sqrt{x}$. | |
| Apr 12, 2016 at 0:17 | history | asked | user45947 | CC BY-SA 3.0 |