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A088865 (Sum of distinct prime factors)^(sum of prime exponents). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 05:10 EDT 2021. Contains 343994 sequences. (Running on oeis4.)