A327500 Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor whose prime multiplicities are distinct (A327498, A327499).

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

Offset: 1

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn

Comments

A number's prime multiplicities are also called its (unsorted) prime signature. Numbers whose prime multiplicities are distinct are A130091.

Examples

			We have 9282 -> 546 -> 42 -> 6 -> 2 -> 1, so a(9282) = 5.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Position of first appearance of n is A002110(n).

Cf. A000005, A056239, A098859, A112798, A124010, A130091, A255231, A327498, A327499, A351564.

Cf. also A327503.

Programs

Mathematica

Table[Length[FixedPointList[#/Max[Select[Divisors[#],UnsameQ@@Last/@FactorInteger[#]&]]&,n]]-2,{n,100}]

PARI

A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
A327499(n) = fordiv(n,d,if(A351564(n/d), return(d)));
A327500(n) = { my(u=A327499(n)); if(u==n, 0, 1+A327500(u)); }; \\ Antti Karttunen, Apr 02 2022

Extensions

Data section extended up to 105 terms by Antti Karttunen, Apr 02 2022