A cute question which I will be working on later today!

Let N be a positive integer and let K is smallest positive integer which doesn't divide N. Now do N = K and repeat this process with this new N. Eventually you will obtain 2.

Define f(N) to denote the length of the resulting sequence.

For example if N = 8, the sequence is 8,3,2. So f(8) = 3.

and if N = 12, the sequence is 12, 5 , 2. So f(12) = 3. Similarly, $ f(6) = 4 $.

The task is compute $ \sum\limits_{i=1} p f(i) = ? $, where p is a natural number.

PS: This is not trivial! Enjoy:)

Question

A cute question which I will be working on later today!

Let N be a positive integer and let K is smallest positive integer which doesn't divide N. Now do N = K and repeat this process with this new N. Eventually you will obtain 2.

Define  f(N)  to denote the length of the resulting sequence.

For example if N = 8, the sequence is 8,3,2. So f(8) = 3.

and if N = 12, the sequence is 12, 5 , 2. So f(12) = 3. Similarly, $ f(6) = 4 $.

The task is compute $  \sum\limits_{i=1} p  f(i)  = ? $, where p is a natural number.

PS: This is not trivial! Enjoy:)

ganeshie8 · Answer

what is $p$

precal · Answer

p is a natural number (stated above)