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A327403
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Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum stable divisor (A327393, A327402).
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0
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0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2
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OFFSET
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1,6
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476. The maximum stable divisor of n is A327393(n).
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LINKS
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EXAMPLE
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We have 798 -> 42 -> 6 -> 2 -> 1, so a(798) = 4.
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MATHEMATICA
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stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[FixedPointList[#/Max[Select[Divisors[#], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&]]&, n]]-2, {n, 100}]
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CROSSREFS
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See link for additional cross-references.
Positions of first appearance of each integer are A325782.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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