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A327500
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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).
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10
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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
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OFFSET
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1,6
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COMMENTS
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A number's prime multiplicities are also called its (unsorted) prime signature. Numbers whose prime multiplicities are distinct are A130091.
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LINKS
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EXAMPLE
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We have 9282 -> 546 -> 42 -> 6 -> 2 -> 1, so a(9282) = 5.
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MATHEMATICA
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Table[Length[FixedPointList[#/Max[Select[Divisors[#], UnsameQ@@Last/@FactorInteger[#]&]]&, n]]-2, {n, 100}]
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PROG
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(PARI)
A351564(n) = issquarefree(factorback(apply(e->prime(e), (factor(n)[, 2]))));
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CROSSREFS
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See link for additional cross-references.
Position of first appearance of n is A002110(n).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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