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A089576
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Let p_k = k-th prime, let f((p_k)^n) = m where m is the largest power of p_(k+1) < (p_k)^n. a(n) = number of iterations of f to reach 1, starting from n and starting from k = 1.
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0
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0, 1, 2, 2, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19
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