A100391 Prime powers which are local minima of A006530.

4, 8, 16, 27, 32, 64, 81, 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1331, 2048, 2187, 2197, 3125, 4096, 6561, 8192, 14641, 15625, 16384, 16807, 19683, 24389, 28561, 32768, 50653, 59049, 65536, 68921, 78125, 79507, 83521, 103823, 117649, 130321

Offset: 1

Author

Labos Elemer, Dec 14 2004

Keywords

• nonn

Examples

			Largest prime factors around 49 are {3,7,5} so 49 is not a member.
k = 343 = 7^3 is in the sequence because the corresponding largest prime factors are {19,7,43}.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006530, A100390.

Programs

Maple

N:= 2*10^5: # to get all terms <= N
f:= proc(x,p)
  if max(numtheory:-factorset(x-1))>p
    and max(numtheory:-factorset(x+1))>p  then x
    fi
end proc:
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

Mathematica

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