A327403 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum stable divisor (A327393, A327402).

0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2

Offset

1,6

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. A number is stable if its distinct prime indices are pairwise indivisible. Stable numbers are listed in A316476. The maximum stable divisor of n is A327393(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Index entries for sequences related to prime indices in the factorization of n.

Example

We have 798 -> 42 -> 6 -> 2 -> 1, so a(798) = 4.

Mathematica

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[FixedPointList[#/Max[Select[Divisors[#], stableQ[PrimePi/@First/@FactorInteger[#], Divisible]&]]&, n]]-2, {n, 100}]

Prog

(PARI) A327403(n) = for(k=0, oo, my(nextn=A327402(n)); if(nextn==n, return(k)); n = nextn); \\ Antti Karttunen, Jan 28 2025

Crossrefs

See link for additional cross-references.

Positions of first appearance of each integer are A325782.

Cf. A000005, A303362, A323014, A327393, A327402.

Sequence in context: A361631 A247462 A323172 * A247371 A331177 A173751

Adjacent sequences: A327400 A327401 A327402 * A327404 A327405 A327406

Keyword

nonn

Author

Gus Wiseman, Sep 15 2019

Extensions

Data section extended to a(105) by Antti Karttunen, Jan 28 2025

Status

approved