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A327407
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Number of steps to reach a fixed point starting with n and repeatedly taking the quotient over the maximum divisor that is 1, prime, or whose prime indices are pairwise coprime. (A327389, A327401).
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9
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0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 2, 1, 1, 2
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OFFSET
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1,9
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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. Numbers that are 1, prime, or whose prime indices are pairwise coprime are listed in A302569.
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LINKS
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EXAMPLE
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We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 4.
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MATHEMATICA
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primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Table[Length[FixedPointList[#/Max[Select[Divisors[#], #==1||PrimeQ[#]||CoprimeQ@@primeMS[#]&]]&, n]]-2, {n, 100}]
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CROSSREFS
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See link for additional cross-references.
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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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