I am not sure where to start: How many ways are there to write 16384 = a_1 * a_2 * a_3 * a_4, a_i are pos. integers, a_i > i for all i ∈ {1,2,3,4}

[jhbalihbfgawlhefb]

I'm not sure if this belongs in the probability / statistics section but I'm not sure where this belongs.
How many ways are there to write 16384 = a_1 * a_2 * a_3 * a_4 where a_i are positive integers and a_i > i for all i ∈ {1, 2, 3, 4}
I'm not really sure what this problem is asking and am not sure where to start

 

[MaxWong]

Note that [imath]16384 = 2^{14}[/imath]. So each [imath]a_i[/imath] must be positive integer powers of 2, this becomes the number of positive integer solutions to the equation [imath]b_1 + b_2 + b_3 + b_4 = 14[/imath], where [imath]b_2 > 1[/imath], [imath]b_3 > 1[/imath], and [imath]b_4 > 2[/imath]. Does this help?

 

[Duplicity]

I'm not sure if this belongs in the probability / statistics section but I'm not sure where this belongs.
How many ways are there to write 16384 = a_1 * a_2 * a_3 * a_4 where a_i are positive integers and a_i > i for all i ∈ {1, 2, 3, 4}
I'm not really sure what this problem is asking and am not sure where to start

Here is a quick start for you:

Sol1: 2*4*8*256
Sol2: 2*4*256*8
Sol3: 2*8*4*256
...
..

Soly1 : 4*8*16*32
Soly2 : 4*8*32*16
...
...

I guess you got the point.

Now try to make these as patterns..