What are the connotations of the words "al-Pi Hashem"?
Rashi: When Moshe asked Hashem how he could possibly enter the Levi'im's tents 1 to find out how many children they had, Hakadosh-Baruch-Hu replied 'You do what you have to do, and leave the rest to Me!' Moshe then went and stood outside the Levi's tents, whilst the Shechinah went in and let him know via a Bas Kol how many children there were in each tent. Therefore the Torah writes "By the mouth of Hashem". 2
Oznayim la'Toorah: Having told Yisrael in 1:29 "Ach es Mateh Levi Lo Sifkod", he needed to inform them here that he was counting them here not on his own volition but "al-Pi Hashem" - since he was not cointing them together with Yisrael but independently.