A112538 If b(n) is the smallest positive integer and c(n) is the largest positive integer such that n = b(n)^c(n), then a(n) = c(n)^b(n).

1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 1, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 1, 1, 32, 1, 27, 1, 1, 1, 1, 25, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 128, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 36, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1024

Offset: 2

Author

Leroy Quet, Dec 14 2005

Keywords

• nonn

Examples

			25 = 5^2, so a(25) = 2^5 = 32.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 2..10000
• G. Kreweras, Sur les hiérarchies de segments, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973). (Annotated scanned copy)

Crossrefs

Cf. A052409, A052410.

Programs

Mathematica

Array[#2^If[#1 == 1, 1, #1^(1/#2)] & @@ {#, Apply[GCD, FactorInteger[#][[All, -1]]]} &, 99, 2] (* Michael De Vlieger, Nov 05 2017, after Ray Chandler at A052409 *)

Formula

a(n) = A052409(n)^A052410(n).

Extensions

Extended by Ray Chandler, Dec 25 2005