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A100391
Prime powers which are local minima of A006530.
1
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
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
Sequence in context: A349112 A325127 A054744 * A122494 A257278 A257279
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 14 2004
STATUS
approved