This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157985 #17 Feb 04 2025 03:49:35
%S A157985 1,-4,-8,-9,-16,-25,-27,-32,36,-49,-64,-81,100,-121,-125,-128,144,
%T A157985 -169,196,216,225,-243,-256,-289,324,-343,-361,400,441,484,-512,-529,
%U A157985 576,-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).
%C A157985 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 A157985 Daniel Forgues, <a href="/A157985/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)) 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. A001597 (perfect powers), A025479 (largest exponents of perfect powers).
%Y A157985 Cf. A025478 (least roots of perfect powers).
%Y A157985 Cf. A157986.
%K A157985 sign
%O A157985 1,2
%A A157985 _Daniel Forgues_, Mar 10 2009