Ah, I assume your referring to the stuff on pg8 of Pomerance's paper, beginning with his Corollary 1, yes?

This does seem similar, but its a little confusing. He says we can partition the Carmichaels into families depending on the ''ratios of the p-1's'' for each p dividing n (I assume these ratio numbers are the same as our sets $\displaystyle u_1,u_2,...,u_k$).

I don't see a proof for this right after, so I figure this must immediately from some other theorem or statement he put above (or elsewhere).

Afterwards, he constructs a set of $\displaystyle a_1,a_2,...,a_n$ which can be used to produce these ''families''. He doesn't say (at least not on pg8) though that his construction actually partitions or generates all the Carmichaels (maybe its implied).

Anyway I haven't read through the whole 26 pgs (and some parts I just skimmed through). Let me know what your thoughts are.