A proof is given of a conjecture, due to F. W. Steutel: the set of positive $\alpha$-values, for which any positive mixture of $\Gamma(\alpha)$-distributions is infinitely divisible, is the interval (0, 2].
"A Proof of Steutel's Conjecture." Ann. Probab. 22 (1) 442 - 452, January, 1994. https://doi.org/10.1214/aop/1176988867