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under Notaion: second sentence, after "the sum or product is over all prime powers with strictly positive exponent (so 1 is not counted)::, formula is missing something.-- GangofOne ( talk) 03:57, 24 May 2014 (UTC)
what I mean is, it says: sigma f(p) , shouldn't that be sigma f(p^k) .... ? GangofOne ( talk) 02:04, 25 May 2014 (UTC)
I take that as a "yes". Fixed. GangofOne ( talk) 03:29, 28 May 2014 (UTC)
In Arithmetic function#Miscellaneous, in the third to fifth lines, on my computer, the passage is very confused. — Preceding unsigned comment added by 38.117.79.31 ( talk) 11:28, 10 July 2014 (UTC)
I have tried making sense of this diagram on two occasions, with no luck. I am considering deleting it. I looked at the history of the user who added it (three years ago) and he had a history of putting original research in articles and was eventually permanently blocked, so I tend to think this is trying to show something from a pet project, rather than some fundamental relationship of BigOmega.
The caption seems to contradict itself multiple times. To be specific, it first refers to the last two binary digits of Ω but then only has two choices, 0 and 1. It then departs from the stated rule by arbitrarily omitting certain primes (and when did this become about the values of the primes instead of just their count?), and then later departs the integers to refer to Gaussian primes, then loses me completely with some odd grammar.
Maybe I'm being a bit harsh; I was actually looking for the distribution of values of Ω mod 2 and at first glance this appears to be it, but reading the full description I don't trust it at all to be what I think it is. Walt ( talk) 22:01, 7 September 2016 (UTC)
There are a few references in the article, e.g. "prime counting functions, which are not arithmetic functions", that imply that arithmetic function should have some precise definition. But the only definition I see of the term is "expresses some arithmetic property of n" which is not precise at all (at least without a link to arithmetic). Is it even a precise term, and if so, what is its definition? Can we make it clearer what the actual definition is? — Preceding unsigned comment added by Luqui ( talk • contribs) 23:50, 7 June 2017 (UTC)
Dear Sapphorain, you asked for sources for the page Arithmetic function (Entropy of a given number with respect to a given multiplicative function . I gave a proof, that is additive, so one does not need additional sources.
Kind regards — Preceding unsigned comment added by 88.69.187.201 ( talk) 16:11, 30 July 2017 (UTC)
I do not understand, why Anita5912 reverted my new table. The new table is much better understandable than the old ones. It contains all functions up to x=4 and explains all the eaxmples in the text.
It also contains the prime factorization of n, which helps readers to understand the formulas. Wolfk.wk ( talk) 17:05, 19 September 2018 (UTC)
Under the heading "First 100 values...", a hyphen is used as a multiplication symbol. — Preceding unsigned comment added by 79.77.163.188 ( talk)
The notion of arithmetic (logarithmic) derivative is an old and well-known notion in number theory. See for instance (1) E. J. Barbeau, Remarks on an arithmetic derivative, Canad. Math. Bull. 4(2), 117–122 (1961); (2)V. Ufnarovski, B. Åhlander, How to differentiate a number, J. Integer Seq. 6, Article 03.3.4 (2003); (3)P. Haukkanen, J. K. Merikoski, T. Tossavainen, On arithmetic partial differential equations, J. Integer Seq. 19, Article 16.8.6 (2016). -- Sapphorain ( talk) 21:08, 18 May 2022 (UTC)
Greetings Wikipedians! The sections listed below violate the Wikipedia:Verifiability policy. They contain no citations to reliable sources.
I'll check this page in 12 months to see if the violation has been remedied. If it hasn't been fixed, I propose to delete all unsourced text. Cordially, BuzzWeiser196 ( talk) 10:55, 29 September 2023 (UTC)
Note that in the table called "First 100 values of some arithmetic functions", there are two functions, both called lambda(n). In the code, one has a capital L and one has a small l. 2A00:23C7:9985:1701:963:1B25:CFBB:3FFA ( talk) 12:46, 10 January 2024 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||
|
This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 10 sections are present. |
under Notaion: second sentence, after "the sum or product is over all prime powers with strictly positive exponent (so 1 is not counted)::, formula is missing something.-- GangofOne ( talk) 03:57, 24 May 2014 (UTC)
what I mean is, it says: sigma f(p) , shouldn't that be sigma f(p^k) .... ? GangofOne ( talk) 02:04, 25 May 2014 (UTC)
I take that as a "yes". Fixed. GangofOne ( talk) 03:29, 28 May 2014 (UTC)
In Arithmetic function#Miscellaneous, in the third to fifth lines, on my computer, the passage is very confused. — Preceding unsigned comment added by 38.117.79.31 ( talk) 11:28, 10 July 2014 (UTC)
I have tried making sense of this diagram on two occasions, with no luck. I am considering deleting it. I looked at the history of the user who added it (three years ago) and he had a history of putting original research in articles and was eventually permanently blocked, so I tend to think this is trying to show something from a pet project, rather than some fundamental relationship of BigOmega.
The caption seems to contradict itself multiple times. To be specific, it first refers to the last two binary digits of Ω but then only has two choices, 0 and 1. It then departs from the stated rule by arbitrarily omitting certain primes (and when did this become about the values of the primes instead of just their count?), and then later departs the integers to refer to Gaussian primes, then loses me completely with some odd grammar.
Maybe I'm being a bit harsh; I was actually looking for the distribution of values of Ω mod 2 and at first glance this appears to be it, but reading the full description I don't trust it at all to be what I think it is. Walt ( talk) 22:01, 7 September 2016 (UTC)
There are a few references in the article, e.g. "prime counting functions, which are not arithmetic functions", that imply that arithmetic function should have some precise definition. But the only definition I see of the term is "expresses some arithmetic property of n" which is not precise at all (at least without a link to arithmetic). Is it even a precise term, and if so, what is its definition? Can we make it clearer what the actual definition is? — Preceding unsigned comment added by Luqui ( talk • contribs) 23:50, 7 June 2017 (UTC)
Dear Sapphorain, you asked for sources for the page Arithmetic function (Entropy of a given number with respect to a given multiplicative function . I gave a proof, that is additive, so one does not need additional sources.
Kind regards — Preceding unsigned comment added by 88.69.187.201 ( talk) 16:11, 30 July 2017 (UTC)
I do not understand, why Anita5912 reverted my new table. The new table is much better understandable than the old ones. It contains all functions up to x=4 and explains all the eaxmples in the text.
It also contains the prime factorization of n, which helps readers to understand the formulas. Wolfk.wk ( talk) 17:05, 19 September 2018 (UTC)
Under the heading "First 100 values...", a hyphen is used as a multiplication symbol. — Preceding unsigned comment added by 79.77.163.188 ( talk)
The notion of arithmetic (logarithmic) derivative is an old and well-known notion in number theory. See for instance (1) E. J. Barbeau, Remarks on an arithmetic derivative, Canad. Math. Bull. 4(2), 117–122 (1961); (2)V. Ufnarovski, B. Åhlander, How to differentiate a number, J. Integer Seq. 6, Article 03.3.4 (2003); (3)P. Haukkanen, J. K. Merikoski, T. Tossavainen, On arithmetic partial differential equations, J. Integer Seq. 19, Article 16.8.6 (2016). -- Sapphorain ( talk) 21:08, 18 May 2022 (UTC)
Greetings Wikipedians! The sections listed below violate the Wikipedia:Verifiability policy. They contain no citations to reliable sources.
I'll check this page in 12 months to see if the violation has been remedied. If it hasn't been fixed, I propose to delete all unsourced text. Cordially, BuzzWeiser196 ( talk) 10:55, 29 September 2023 (UTC)
Note that in the table called "First 100 values of some arithmetic functions", there are two functions, both called lambda(n). In the code, one has a capital L and one has a small l. 2A00:23C7:9985:1701:963:1B25:CFBB:3FFA ( talk) 12:46, 10 January 2024 (UTC)