  We extend the Euler's totient function (from arithmetic) to any irreducible
subfactor planar algebra, using the Mobius function of its biprojection
lattice, as Hall did for the finite groups. We prove that if it is nonzero then
there is a minimal 2-box projection generating the identity biprojection. We
explain a relation with a problem of K.S. Brown. As an application, we define
the dual Euler totient of a finite group and we show that if it is nonzero then
the group admits a faithful irreducible complex representation. We also get an
analogous result at depth 2, involving the central biprojection lattice.
