f(N)=[N/1] + [N/2] + [N/3]+ ....+ [N/N] . Find f(64)-f(63).

If you could reason carefully you see f(N+1)-f(N)=no. of factors og N+1.

Because only for these numbers(factors of N+1) ; [N+1/these no.]=[N/these no.]+1.

You could verify it for any no. N.

f(64)-f(63)=7  ;{factors of 64 are 1,2,4,8,16,32,64}.