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

1,9

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.

Sequence in context: A326297 A060128 A330751 * A290104 A308479 A031280

Adjacent sequences: A327404 A327405 A327406 * A327408 A327409 A327410

Keyword

nonn

Author

Gus Wiseman, Sep 20 2019

Status

approved