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 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). 3

%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(m-1)) 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 a(n) = A001597(n) * (-1)^(Pi(m) - Pi(m-1)), 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

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Last modified September 26 16:15 EDT 2021. Contains 347670 sequences. (Running on oeis4.)