  For each of the simple Lie algebras $\mathfrak{g}=A_l$, $D_l$ or $E_6$, we
show that the all-genera one-point FJRW invariants of $\mathfrak{g}$-type,
after multiplication by suitable products of Pochhammer symbols, are the
coefficients of an algebraic generating function and hence are integral.
Moreover, we find that the all-genera invariants themselves coincide with the
coefficients of the unique calibration of the Frobenius manifold of
$\mathfrak{g}$-type evaluated at a special point. For the $A_4$ (5-spin) case
we also find two other normalizations of the sequence that are again integral
and of at most exponential growth, and hence conjecturally are the Taylor
coefficients of some period functions.
