A088865 (Sum of distinct prime factors)^(sum of prime exponents).

1, 2, 3, 4, 5, 25, 7, 8, 9, 49, 11, 125, 13, 81, 64, 16, 17, 125, 19, 343, 100, 169, 23, 625, 25, 225, 27, 729, 29, 1000, 31, 32, 196, 361, 144, 625, 37, 441, 256, 2401, 41, 1728, 43, 2197, 512, 625, 47, 3125, 49, 343, 400, 3375, 53, 625, 256, 6561, 484, 961

Offset: 1

Author

Reinhard Zumkeller, Nov 26 2003

Keywords

• nonn

Comments

a(n) = n iff n is 1 or a prime power; otherwise, a(n) > n. - Ivan Neretin, May 31 2016

Examples

			a(75) = a(3^1 * 5^2) = (3+5)^(1+2) = 8^3 = 512.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Programs

Mathematica

pf2pe[n_]:=Module[{tfi=Transpose[FactorInteger[n]]},Total[ First[tfi]]^ Total[ Last[tfi]]]; Array[pf2pe,60] (* Harvey P. Dale, Sep 21 2011 *)
Array[Power @@ Map[Total, Transpose@ FactorInteger@ #] &, 58] (* Michael De Vlieger, Apr 25 2017 *)

Formula

a(n) = A008472(n)^A001222(n).