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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).
10
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.
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. also A327503.
Sequence in context: A374470 A353507 A362613 * A351946 A351944 A366918
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2019
EXTENSIONS
Data section extended up to 105 terms by Antti Karttunen, Apr 02 2022
STATUS
approved