A327401 -id:A327401

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A327407

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).

+20
9

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

1,9

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

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

MATHEMATICA

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}]

CROSSREFS

See link for additional cross-references.

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

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 20 2019

STATUS

approved

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