All Questions
4
questions
2
votes
2
answers
144
views
Finding positive integer $n>10$ that maximizes $\frac{\sigma_0(n)}{2^{\log n}}$
Among all the positive integer, which one integer, $n$, can make the number below the largest?
$$f(n)=\frac{\sigma_0(n)}{2^t}$$where $t=\log_{10}n$ and $\sigma_0$ is the divisor function.
For example,...
- 183
1
vote
4
answers
98
views
When $f(x)=\frac{-b^2m-ba+ax}{-mx-bm-a}$ is an integer
$a,b,m,x$ are positive integers.
For which $x>0$ is $f(x)$ an integer?
$$f(x)=\frac{-b^2m-ba+ax}{-mx-bm-a}$$
I been trying to play with it, I changed it to:
$$\frac{b^2m-a\left(b+x\right)}{a+m\...
- 1,450
1
vote
1
answer
73
views
When $f(x) = \frac{ax + b}{a -x + 1}$ is an integer
Given that $a$ and $b$ are positive integers. and $$f(x) = \frac{ax + b}{a -x + 1}$$ is an integer, what integer values can x have?
If I could only somehow move $x$ from numerator to the denominator ...
- 1,450
6
votes
2
answers
9k
views
Total number of divisors of factorial of a number
I came across a problem of how to calculate total number of divisors of factorial of a number. I know that total number of divisor of a number $n= p_1^a p_2^b p_3^c $ is $(a+1)*(b+1)*(c+1)$ where $a,...
- 298