  An explicit computation of the so-called string-theoretic E-function of a
normal complex variety X with at most log-terminal singularities can be
achieved by constructing one snc-desingularization of X, accompanied with the
intersection graph of the exceptional prime divisors, and with the precise
knowledge of their structure. In the present paper, it is shown that this is
feasible for the case in which X is the underlying space of a class of
absolutely isolated singularities (including both usual A_{n}-singularities and
Fermat singularities of arbitrary dimension). As byproduct of the exact
evaluation of e_{str}(X), for this class of singularities, one gets (in
contrast to the expectations of V1!) counterexamples to a conjecture of Batyrev
concerning the boundedness of the string-theoretic index. Finally, the
string-theoretic Euler number is also computed for global complete
intersections in P^{N} with prescribed singularities of the above type.
