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

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn

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).

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Gus Wiseman, Sequences counting and encoding certain classes of multisets.

Crossrefs

See link for additional cross-references.

Cf. A000005, A000961, A005117, A006530, A007947, A071625, A072774, A112798, A327528.

Programs

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 *)

Formula

a(n) = n / A327528(n). - Amiram Eldar, Dec 19 2023