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We have 441 -> 63 -> 9 -> 3 -> 1, so a(441) = 4.

Number of steps to reach a fixed point starting with n a and repeatedly taking the quotient over the maximum prime divisor that is 1, prime, or whose prime indices are pairwise coprime. (A327389, A327401).

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.

allocated for Gus WisemanNumber of steps to reach a fixed point starting with n a repeatedly taking the quotient over the maximum prime divisor that is 1, prime, or whose prime indices are pairwise coprime. (A327389, A327401).

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

1,9

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 A302569.

Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>

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}]

See link for additional cross-references.

Cf. A000005, A006530, A056239, A112798, A302569, A304711.

allocated

nonn

Gus Wiseman, Sep 20 2019

approved

editing

allocated for Gus Wiseman

allocated

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