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Abelian orders of hereditarily finite transitive sets.

Sequence (submitted): 1, 2, 3, 6, 12, 2^13868 * 3^7873 * 5^2012 * 7^1911, …

Conjecture: a(7) has a closed form (submitted). a(7) = 2^a ⋅ 3^b ⋅ 5^c ⋅ 7^d ⋅ 11^e ⋅13^f ⋅ ... ⋅ P^z.

Try to prove / disprove... (or to compute a(7)...)