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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Gus Wiseman, Sequences counting and encoding certain classes of multisets.

Formula

a(n) = n / A327526(n). - Amiram Eldar, Dec 19 2023

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}]
a[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; n / Max@ Table[(Times @@ p[[Position[e, _?(# >= k &)] // Flatten]])^k, {k, Union[e]}]]; Array[a, 100] (* Amiram Eldar, Dec 19 2023 *)

Crossrefs

See link for additional cross-references.

Cf. A000005, A000961, A005117, A006530, A007947, A071625, A072774, A112798, A327526.

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

approved