Timeline for The number of totatives to the nth primorial, in an interval shorter than the nth primorial
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Sep 10, 2015 at 20:13 | comment | added | Gerhard Paseman | Also, sometimes it helps marginally to fudge on m: if you can pick m to be one less but have 1 - sum > 1/2p_m, that will also work. In any case for large m (m > 3) we can have both m^e < n and \phi(M)4 log m > M while keeping (1 - sum) comfortably large. Gerhard "And Always Weaken The Inequality" Paseman, 2015.09.10 | |
| Sep 10, 2015 at 19:54 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
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| Sep 10, 2015 at 19:22 | comment | added | Gerhard Paseman | This is posted primarily in response to the last conjectured inequality in the question, which for large n is true, but limits d to (for large n) some value greater than n/4. It is quite possible that d can actually be as small as 2, but no one has seen a proof for all n> 2. More generally, given an integer N with two distinct largest prime factors p and q, I know nothing contradicting the conjecture that two totatives to N exist in an interval of length pq. Gerhard "You Saw It Here First" Paseman, 2015.09.10 | |
| Sep 10, 2015 at 18:46 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
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| Sep 10, 2015 at 18:41 | history | answered | Gerhard Paseman | CC BY-SA 3.0 |