APL (Dyalog), 50 2929 25 bytes
Look 'ma, no built-in totient!
4 bytes saved thanks to @H.PWiz
0{⍵=1:⍺⋄(⍺+1)∇+0⋄1+∇+/1=⍵∨⍳⍵}¨1+⍳99 How?
Apparently I went for the longer (and harder) totient formula first. See revisions history.
⍳⍵ - 1 to n
⍵∨ - gcd with n
1= - equal to 1?
+/ - sum 'em all
This is the totient. All the rest is wrapper for the counting (1+∇) and applying on the range 2..100 (¨1+⍳99).