%I A157985
%S A157985 1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,144,169,
%T A157985 196,216,225,243,256,289,324,343,361,400,441,484,512,529,576,
%U A157985 625,676,729,784,841,900,961,1000,1024,1089,1156,1225,1296,1331
%V A157985 1,-4,-8,-9,-16,-25,-27,-32,36,-49,-64,-81,100,-121,-125,-128,144,-169,
%W A157985 196,216,225,-243,-256,-289,324,-343,-361,400,441,484,-512,-529,576,
%X A157985 -625,676,-729,784,-841,900,-961,1000,-1024,1089,1156,1225,1296,-1331
%N A157985 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).
%H A157985 Daniel Forgues, <a href="b157985.txt">Table of n, a(n) for n=1..10000</
               a>
%F A157985 a(n) = {m^k}_n * (-1)^{Pi(m) - Pi(m-1)}
%F A157985 where {m^k}_n is the n_th 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 A157985 a(n) = {A001597(n)} * (-1)^{Pi(m) - Pi(m-1)}, with m = {A001597(n)}^{1/
               {A025479(n)}}.
%Y A157985 Cf. A157986 Largest exponents of perfect powers (m^k where m is an integer 
               and k >= 2) multiplied by -1 when base m is prime (m^k thus a prime 
               power).
%Y A157985 Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
%Y A157985 Cf. A025479 Largest exponents of perfect powers (A001597).
%Y A157985 Cf. A025478 Least roots of perfect powers (A001597). [From Daniel Forgues 
               (squid(AT)zensearch.com), Mar 14 2009]
%Y A157985 Sequence in context: A158804 A080366 A001694 this_sequence A001597 A072777 
               A076292
%Y A157985 Adjacent sequences: A157982 A157983 A157984 this_sequence A157986 A157987 
               A157988
%K A157985 sign
%O A157985 1,2
%A A157985 Daniel Forgues (squid(AT)zensearch.com), Mar 10 2009