Numbers 1:3 says the census is for men above the age of 20. I have this fact in my head that it was only for those below the age of 60. Is that true? If so, where is the source?
By the Meraglim, the decree was that "in this desert, your carcasses will fall, for all of your countings and all of your numbers, from the age of 20 and older..." (Bamidbar 14:29).
The Gemara (Bava Basra 121b) derives by a gezeirah shavah - the common usage of "and older" here and by Erchin (Vayikra 27:7) - that the decree was for 20 to 60. As this was according to their countings, which Rashi to the above passuk in Bamidbar1 explains to refer to anyone counted in the original census, it must be that that census was from 20 to 60 as well.
1The reason I quote Rashi and not the Gemara in Bava Basra is because the Gemara ultimately rejected that. Apparently Rashi learns that it still stands, but that there are exceptions.