%I
%S 1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,144,
%T 169,196,216,225,243,256,289,324,343,361,400,441,484,512,529,
%U 576,625,676,729,784,841,900,961,1000,1024,1089,1156,1225,1296,1331
%N Perfect powers (m^k where m is an integer and k >= 2) multiplied by 1 when m is prime for largest k (m^k thus a prime power).
%C The rather strange phrase "largest k" in the definition refers to the fact that there can be several ways to write a number in the form m^k.  _N. J. A. Sloane_, Jan 01 2019
%H Daniel Forgues, <a href="/A157985/b157985.txt">Table of n, a(n) for n=1..10000</a>
%F a(n) = {m^k}_n * (1)^(Pi(m)  Pi(m1)) where {m^k}_n is the nth perfect power with positive integer base m corresponding to largest integer exponent k and Pi(m) is the prime counting function evaluated at m.
%F a(n) = A001597(n) * (1)^(Pi(m)  Pi(m1)), with m = A001597(n)^(1/{A025479(n)).
%Y Cf. A001597 (perfect powers), A025479 (largest exponents of perfect powers.
%Y Cf. A025478 (least roots of perfect powers).
%Y Cf. A157986.
%K sign
%O 1,2
%A _Daniel Forgues_, Mar 10 2009
