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A327528 revision #5

A327528

Quotient of n over the maximum uniform divisor of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1

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OFFSET

1,12

COMMENTS

Requires A071625(n) steps to reach 1, the only fixed point.

A number is uniform if its prime multiplicities are all equal, meaning it is a power of a squarefree number. Uniform numbers are listed in A072774. The maximum uniform divisor of n is A327526(n).

LINKS

Table of n, a(n) for n=1..87.

Gus Wiseman, Sequences counting and encoding certain classes of multisets

EXAMPLE

The uniform divisors of 40 are {1, 2, 4, 5, 8, 10}, so a(40) = 40/10 = 4.

MATHEMATICA

Table[n/Max[Select[Divisors[n], SameQ@@Last/@FactorInteger[#]&]], {n, 100}]

CROSSREFS

See link for additional cross-references.

Cf. A000005, A000961, A005117, A006530, A007947, A071625, A112798.

Sequence in context: A276088 A030612 A371921 * A264857 A370645 A340596

Adjacent sequences: A327525 A327526 A327527 * A327529 A327530 A327531

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 17 2019

STATUS

proposed