Lie algebra

There is a function μ: ℕ → ℕ, such that any, all of whose subalgebras are n-step subideals, is nilpotent of class ≤ μ(n). It is defined by:


 * μ₁(c,d) = cd + (c-1)(d-1)
 * μ₂(r,s) = s + s² + … + sʳ
 * μ₃(n) = μ₂(n²,n)
 * μ₄(n,1) = 1
 * μ₄(n,2) = μ₃(n)
 * μ₄(n,d) = ab + (a-1)(b-1), where a = μ₃(n) and b = μ₄(n,d-1)
 * μ₅(n) = n - 1 + μ₂(n,n)
 * μ₆(n) = n μ₅(n)
 * μ(1) = 1
 * μ(n) = μ₄(n, μ₆(1 + μ₄(n, (n-1) μ(n-1))))