Some remarks on small values of $$\tau (n)$$

A natural variant of Lehmer’s conjecture that the Ramanujan $$\tau $$ -function never vanishes asks whether, for any given integer $$\alpha , there exist $$n \in \mathbb {Z}^+$$ such (n) = \alpha . series recent papers excludes many integers as possible values using theory primitive divisors Lucas numbers, computations points on curves, and congruences (n)$$ We synthesize these results methods to prove if $$0< \left| \right| < 100$$ \notin T := \{2^k, -24,-48, -70,-90, 92, -96\}$$ then \ne all > 1$$ Moreover, T$$ n is square-free with prescribed prime factorization. Finally, we show a strong form Atkin-Serre implies $$\left| \tau 2$$