Inspirations for this paper can be traced to Urbanik [48] where convolution semigroups of multiple decomposable distributions were introduced. In particular, the classical gamma G t and log G t , t > 0 variables are selfdecomposable. In fact, we show that log G t is twice selfdecomposable if, and only if, t ≥ t 1 ≈ 0.15165. Moreover, we provide several new factorizations of the Gamma function and the Gamma distributions. To this end, we revisit the class of multiply selfdecomposable distributions, denoted L n (R), and propose handy tools for its characterization, mainly based on the Mellin-Euler's differential operator. Furthermore, we also give a perspective of generalization of the class L n (R) based on linear operators or on stochastic integral representations.