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Sur la fonction «nombre de facteurs premiers de n»
| Content Provider | Semantic Scholar |
|---|---|
| Author | Erdös, Paul Nicolas, Jean-Louis |
| Copyright Year | 1979 |
| Abstract | Let w (n) be the number of prime factors of n ; n is said w-largely composite if m < n => w (m) < w (n) . The quantity Q, (X) of such numbers < X verifies e`l ~" '91 < QI (X) < e`z "9 x Then we prove card n < x I e )(n) > c log x = x i+o(1) log log x and if Q (n) is the total number of prime factors of n counted according to multiplicity, Q (n) + Q (n + 1) < log l0 n (1+0(l» . g An integer n is defined w-interesting if m > n w(m) < w (n) . m n A short study of these numbers is given. We prove that there exists infinitely many strangulation points (nk ) for the function n w (n) i .e . such that : m < nk => m w (m) < n k w (n k) and m > nk => m w (m) > nk w (nk) Finally, we deduce from some formula of A . Selberg the exact order of card {n < x I w (n) > a log log x} for cc > 1 . |
| Starting Page | 1 |
| Ending Page | 19 |
| Page Count | 19 |
| File Format | PDF HTM / HTML |
| Volume Number | 20 |
| Alternate Webpage(s) | http://www.numdam.org/article/SDPP_1978-1979__20_2_A9_0.pdf |
| Alternate Webpage(s) | https://users.renyi.hu/~p_erdos/1981-34.pdf |
| Alternate Webpage(s) | http://www.math-inst.hu/~p_erdos/1981-34.pdf |
| Alternate Webpage(s) | http://www.renyi.hu/~p_erdos/1981-34.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
