cp's OEIS Frontend

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.

A157987 Smallest roots m of perfect powers (m^k where m is an integer and k >= 2) multiplied by -1 when m is prime (m^k thus a prime power).

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%I A157987 #4 Mar 31 2012 14:01:22
%S A157987 1,-2,-2,-3,-2,-5,-3,-2,6,-7,-2,-3,10,-11,-5,-2,12,-13,14,6,15,-3,-2,
%T A157987 -17,18,-7,-19,20,21,22,-2,-23,24,-5,26,-3,28,-29,30,-31,10,-2,33,34,
%U A157987 35,6,-11,-37,38,39,40,-41,12,42,-43,44,45,-2,46,-3,-13,-47,48,-7,50,51,52
%N A157987 Smallest roots m of perfect powers (m^k where m is an integer and k >= 2) multiplied by -1 when m is prime (m^k thus a prime power).
%H A157987 Daniel Forgues, <a href="/A157987/b157987.txt">Table of n, a(n) for n=1..10000</a>
%F A157987 a(n) = {m}_n * (-1)^{Pi(m) - Pi(m-1)}
%F A157987 where {m}_n is the smallest root of {m^k}_n (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 A157987 a(n) = m * (-1)^{Pi(m) - Pi(m-1)}, with m = A025478(n) = {A001597(n)}^{1/{A025479(n)}}.
%Y A157987 Cf. 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).
%Y A157987 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 A157987 Cf. A001597 Perfect powers: m^k where m is an integer and k >= 2.
%Y A157987 Cf. A025479 Largest exponents of perfect powers (A001597).
%Y A157987 Cf. A025478 Least roots of perfect powers (A001597).
%K A157987 sign
%O A157987 1,2
%A A157987 _Daniel Forgues_, Mar 10 2009, Mar 14 2009