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

1,1

Links

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

Example

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}.

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

<<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]

Crossrefs

Cf. A006530, A100390.

Sequence in context: A349112 A325127 A054744 * A122494 A257278 A257279

Adjacent sequences: A100388 A100389 A100390 * A100392 A100393 A100394

Keyword

nonn

Author

Labos Elemer, Dec 14 2004

Status

approved