Revision as of 23:01, 5 August 2015 edit 2601:445:4001:4514:85a3:3283:72dc:2303 (talk) An essay toward rectifying the most thorough neglect of standard usage conventions that's happened in this part of the Universe in a long long time. ← Previous edit		Revision as of 23:02, 5 August 2015 edit undo 2601:445:4001:4514:85a3:3283:72dc:2303 (talk) →Calculating mean values using Dirichlet series: etc........ Next edit →
Line 44: For an integer ''k'' ≥ 1 the set ''Q<sub>k</sub>'' of '''''k''-th-power-free''' integers is : <math>~~Q_{k}~~Q_k :=\{n \in \mathbb{Z}\|\;mid n \text{ is not divisible by } d^k \text{ for any integer } d\ge 2\}.</math>. We calculate the [[natural density]] of these numbers in {{math\|'''N'''}}, that is, the average value of [[indicator function\|'''1<sub>''Q''<sub>''k''</sub></sub>''']], denoted by ''δ''(''n''), in terms of the [[zeta function]].

Average order of an arithmetic function: Difference between revisions