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A100393
Composite numbers k such that Gpf(k-1) < Gpf(k) > Gpf(k+1), where Gpf = A006530.
2
26, 34, 49, 51, 55, 65, 69, 76, 86, 94, 99, 111, 116, 118, 122, 129, 134, 142, 146, 155, 161, 183, 185, 188, 202, 206, 209, 214, 218, 237, 244, 246, 249, 254, 265, 267, 274, 287, 291, 295, 298, 302, 305, 309, 321, 326, 329, 334, 339, 341, 344, 351, 356, 362
OFFSET
1,1
COMMENTS
A006530(k) is the largest prime factor of k.
LINKS
EXAMPLE
26 is in the sequence because the largest prime factors of 25, 26, and 27 are 5, 13, and 3, respectively.
MAPLE
gpf:= n -> max(numtheory:-factorset(n)):
L:= map(gpf, [$1..1000]):
select(t -> L[t]<> t and L[t]>L[t-1] and L[t]>L[t+1], [$2..nops(L)-1]); # 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[s, s1]&&Greater[s, s2]&&!PrimeQ[n], Print[{n, {s1, s, s2}}]; ta=Append[ta, n]], {n, 1, 1000}]; ta=Delete[ta, 1]
Select[Flatten[Position[Partition[Table[FactorInteger[n][[-1, 1]], {n, 400}], 3, 1], _?(#[[1]]< #[[2]]> #[[3]]&), 1, Heads->False]], CompositeQ[#+1]&]+1 (* Harvey P. Dale, May 10 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Dec 14 2004
EXTENSIONS
Edited by Don Reble, Jun 13 2007
STATUS
approved