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A327526
Maximum uniform divisor of n.
9
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).
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.
Sequence in context: A373231 A334684 A062759 * A121758 A121759 A265310
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 16 2019
STATUS
approved