Let me expand a bit on what John Conway said:
Sublattices of index n in a 2-dim. lattice are in one-one
correspondence with matrices
a b
0 d
with a>0, ad=n, b in [0..d-1]
The number of these is Sum_{d|n} = sigma(n), which is A000203.
A sublattice is primitive if gcd(a,b,d) = 1; the number
of these is n * product_{p|n} (1+1/p), which is A001615.