This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Set of orders of elements of A_8 X A_8 is {1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 105}, thus a(8)=19.
From _Joerg Arndt_, Dec 04 2022: (Start) The 15 partitions of 7 are the following: [ #] [ partition ] lcm( parts ) [ 1] [ 1 1 1 1 1 1 1 ] 1 [ 2] [ 1 1 1 1 1 2 ] 2 [ 3] [ 1 1 1 1 3 ] 3 [ 4] [ 1 1 1 2 2 ] 2 [ 5] [ 1 1 1 4 ] 4 [ 6] [ 1 1 2 3 ] 6 [ 7] [ 1 1 5 ] 5 [ 8] [ 1 2 2 2 ] 2 [ 9] [ 1 2 4 ] 4 [10] [ 1 3 3 ] 3 [11] [ 1 6 ] 6 [12] [ 2 2 3 ] 6 [13] [ 2 5 ] 10 [14] [ 3 4 ] 12 [15] [ 7 ] 7 The maximum value attained is 7 * 12, so a(7) = 84. (End)
x=[{1},{1}]
for i in range(2,40):
u=[]
for j in range(1,i):
u.extend([k*j//math.gcd(k,j) for k in x[i-j]])
x.append(set(u))
xx=[set([i*j//math.gcd(i,j) for i in t for j in t]) for t in x]
print([max(i) for i in xx][2:])
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