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First hint to puzzle 152: Totient valence

A number of steps are needed to evaluate v(21000)...

Note that, if k = p1a1 · p2a2 ·...· prar, then phi(k) = (p1a1 − p1a1−1)·(p2a2 − p2a2−1)·...·(prar − prar−1).

Show that: