Saw this in the EIS:

ID Number: A054396
Sequence:  28,30,44,63,66,70,76,92
Name:      There are precisely 4 groups of order n.
See also:  Cf. A000001, A003277, A054395-...
Keywords:  nonn
Offset:    1
Author(s): njas, May 21 2000
Extension: I would also like to get the analogous sequence with 4 replaced by 3. It
           begins 75, ...


The sequence for 3 begins 75,363,609,867

I think it would continue 1183,1265,1275,1491,1587,1725

and I think the formula is numbers of the form:

q^2*p_1*p_2*...*p_n (all primes) where there is exatly one p_i that divides
q+1 and no p_i that divides q-1 and no p_i,p_j where p_i divides p_j-1

or

p_1*p_2*...*p_n where for some 1<=i<j<k<=n, p_i divides p_j-1 and p_j divides
p_k-1 and no other p_i,p_j such that p_i divides p_j-1.

But I don't no my group enumeration formulas backward and forward, so if
someone who knows group theory well could verify the results, I would
appreciate it.

Christian