The children of Israel were a peculiar people, a people who were for God and thus stood apart from the nations. Among this peculiar people there was an extraordinary tribe—the Levites—and this tribe was not numbered among the sons of Israel. The Levites were the tribe which was closest to God and which served God as the replacement of all the Israelites.
In verses 57 through 62 we have the numbering of the Levites, who were not to have a portion of the land. "Those numbered of them were twenty-three thousand, every male from a month old and above; for they were not numbered among the sons of Israel, because there was no inheritance given to them among the sons of Israel" (v. 62).
Among all those who were included in the second numbering, none had been in the first numbering, except Caleb and Joshua. This means that only Caleb and Joshua were numbered twice. With the exception of these two, all those in the first numbering, including Moses and Aaron, were not in the renumbering.