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

1,6

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

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

Mathematica

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

Prog

(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

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.

Sequence in context: A374470 A353507 A362613 * A351946 A351944 A366918

Adjacent sequences: A327497 A327498 A327499 * A327501 A327502 A327503

Keyword

nonn

Author

Gus Wiseman, Sep 16 2019

Extensions

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

Status

approved