A327526 Maximum uniform divisor of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 13, 14, 15, 16, 17, 9, 19, 10, 21, 22, 23, 8, 25, 26, 27, 14, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 16, 49, 25, 51, 26, 53, 27, 55, 14, 57, 58, 59, 30, 61, 62, 21, 64, 65, 66, 67, 34

Offset

1,2

Comments

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 number of uniform divisors of n is A327527(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 / A327528(n). - Amiram Eldar, Dec 19 2023

Example

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

Mathematica

Table[Max[Select[Divisors[n], SameQ@@Last/@FactorInteger[#]&]], {n, 100}]
a[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; 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, A327528.

Sequence in context: A278063 A334684 A062759 * A121758 A121759 A265310

Adjacent sequences: A327523 A327524 A327525 * A327527 A327528 A327529

Keyword

nonn

Author

Gus Wiseman, Sep 16 2019

Status

approved