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A100391 Prime powers which are local minima of A006530.

%I A100391 #9 Jul 13 2018 05:20:20
%S A100391 4,8,16,27,32,64,81,125,128,243,256,343,512,625,729,1024,1331,2048,
%T A100391 2187,2197,3125,4096,6561,8192,14641,15625,16384,16807,19683,24389,
%U A100391 28561,32768,50653,59049,65536,68921,78125,79507,83521,103823,117649,130321
%N A100391 Prime powers which are local minima of A006530.
%H A100391 Robert Israel, <a href="/A100391/b100391.txt">Table of n, a(n) for n = 1..1000</a>
%e A100391 Largest prime factors around 49 are {3,7,5} so 49 is not a member.
%e A100391 k = 343 = 7^3 is in the sequence because the corresponding largest prime factors are {19,7,43}.
%p A100391 N:= 2*10^5: # to get all terms <= N
%p A100391 f:= proc(x,p)
%p A100391   if max(numtheory:-factorset(x-1))>p
%p A100391     and max(numtheory:-factorset(x+1))>p  then x
%p A100391     fi
%p A100391 end proc:
%p A100391 sort([seq(seq(f(p^i,p),i=2..floor(log[p](N))),p=select(isprime, [2,seq(i,i=3..floor(sqrt(N)),2)]))]); # _Robert Israel_, Jul 12 2018
%t A100391 <<NumberTheory`NumberTheoryFunctions` mxp[x_] :=Max[PrimeFactorList[x]]; lf[x_] :=Length[PrimeFactorList[x]]; ta={{0}};Do[s1=mxp[n-1];s=mxp[n];s2=mxp[n+1]; If[Greater[s1, s]&&Greater[s2, s]&&Equal[lf[n], 1], Print[{n, {s1, s, s2}}];ta=Append[ta, n]], {n, 1, 512}];ta=Delete[ta, 1]
%Y A100391 Cf. A006530, A100390.
%K A100391 nonn
%O A100391 1,1
%A A100391 _Labos Elemer_, Dec 14 2004