On the ϰϰth root of a Stieltjes moment sequence

Stieltjes moment sequences {an}n=0∞ whose ϰϰth roots {anϰ}n=0∞ are Stieltjes moment sequences are studied (ϰϰ is a fixed integer greater than or equal to 22). A formula connecting the closed supports of representing measures of {an}n=0∞ and {anϰ}n=0∞ is established. The relationship between the holes of the supports of these measures is investigated. The set of all pairs (M,N)(M,N) of positive integers for which there exists a Stieltjes moment sequence whose square root is a Stieltjes moment sequence and both of them have representing measures supported on subsets of (0,∞)(0,∞) of cardinality MM and NN, respectively, is described.