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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).
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
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.
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.
Sequence in context: A326297 A060128 A330751 * A290104 A308479 A031280
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 20 2019
STATUS
approved