Timeline for How many integers are of the form $n/d(n)$, where $d(n)$ is the number of divisors of $n$?
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8 events
| when toggle format | what | by | license | comment | |
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| Jun 3, 2014 at 2:30 | comment | added | Shivam Patel | @Lucia sorry ..I did not see the list ...just as a curiosity so can you tell me the distribution of numbers in form $10n$ in the sequence | |
| Jun 3, 2014 at 2:28 | comment | added | Lucia | @ShivamPatel: Not true -- $810$, $840$, $960$ etc. I'm afraid I don't know any more about this sequence! | |
| Jun 3, 2014 at 2:26 | comment | added | Shivam Patel | @Lucia can you prove that if the number in the list is in the form $15n$ then $n$ is a prime. | |
| Jun 3, 2014 at 2:25 | comment | added | Shivam Patel | @Lucia extremely good proof | |
| Jun 3, 2014 at 2:16 | comment | added | Lucia | Here is a variant of your construction which produces many excluded numbers. I claim that if $p$ (a prime) is large then $15p$ fails the conjecture. For if $n=15pd(n)$ and $p$ is large then $p$ can divide $n$ only to the power $1$ (use $d(n)\le n^{1/3}$ for large $n$). If now $n=pm$ with $(p,m)=1$ then we must have $m=30d(m)$, contradicting Greg Martin's result that $30$ is excluded. In fact, inspecting his table it looks like $15p$ is excluded for all primes $p>5$. | |
| Jun 2, 2014 at 21:40 | history | edited | Tony Huynh | CC BY-SA 3.0 |
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| Jun 2, 2014 at 21:27 | history | edited | Tony Huynh | CC BY-SA 3.0 |
added 1 character in body
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| Jun 2, 2014 at 20:13 | history | answered | Tony Huynh | CC BY-SA 3.0 |