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).

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

Offset: 1

Author

Gus Wiseman, Sep 20 2019

Keywords

• nonn

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.

Examples

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

Links

• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

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

Programs

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}]