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

1,2

Comments

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

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Sequence in context: A248713 A242799 A281588 * A237342 A075807 A124232

Adjacent sequences: A088862 A088863 A088864 * A088866 A088867 A088868

Keyword

nonn

Author

Reinhard Zumkeller, Nov 26 2003

Status

approved