A327402 -id:A327402 - cp's OEIS frontend

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

Gus Wiseman, Sep 15 2019

nonn

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).

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

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.

See link for additional cross-references.
Positions of first appearance of each integer are A325782.
Cf. A000005, A303362, A323014, A327393, A327402.

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}]

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

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

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions