  Algebraic knots are known to be iterated torus knots and to admit L-space
surgeries. However, Hedden proved that there are iterated torus knots that
admit L-space surgeries but are not algebraic. We present an infinite family of
such examples, with the additional property that no nontrivial linear
combination of knots in this family is concordant to a linear combination of
algebraic knots. The proof uses the Ozsvath-Stipsicz-Szabo Upsilon function,
and also introduces a new invariant of L-space knots, the formal semigroup.
