All About $\color{#D61F06}{2}$ prime

Number Theory Level pending

$\textit{If}$ $\implies$ $K_2$ (X) =How many times can X be divided by $\color{#D61F06}{2}$

For Example :-

$K_2$ (8)=3

$K_2$ (3)=0

For Example :-

B(3)=The Sum of the ones in binary of 3 which is (11) =2

B(6)=(110) =2

B(13)=(1101)=3

B(10)=2

If $\displaystyle\sum_{n=1} ^X$ ( $K_2$ (n) ) =99B(x)

What is X=?

No awnser is right 101B(X) 97B(X) 100B(X) 98B(X)

1 solution

Ahmed Pro
Jul 29, 2020

$\boxed{Equation 1}$ $\displaystyle\sum_{n=1} ^X$ ( $K_2(n)$ ) = X-B(X)

By replacing $\displaystyle\sum_{n=1} ^X$ ( $K_2(n)$ ) with 99B(X)

So 99B(X)=X-B(X)