A100393 Composite numbers k such that Gpf(k-1) < Gpf(k) > Gpf(k+1), where Gpf = A006530.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A006530, A100390, A100392.

Sequence in context: A119481 A232668 A349733 * A133635 A167705 A061673

Adjacent sequences: A100390 A100391 A100392 * A100394 A100395 A100396

Keyword

nonn

Author

Labos Elemer, Dec 14 2004

Extensions

Edited by Don Reble, Jun 13 2007

Status

approved