A076763 1-apexes of omega: numbers n such that omega(n-1) < omega(n) > omega(n+1), where omega(m) = the number of distinct prime factors of m.

6, 10, 12, 18, 24, 26, 28, 30, 42, 48, 60, 66, 70, 72, 78, 80, 82, 84, 90, 102, 105, 108, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 192, 195, 198, 204, 210, 220, 222, 228, 234, 238, 240, 242, 246, 252, 255

Offset

1,1

Comments

I call n a "k-apex" (or "apex of height k") of the arithmetical function f if n satisfies f(n-k) < ... < f(n-1) < f(n) > f(n+1) > .... > f(n+k).

The terms here are the positions of the positive terms in A101941. Note, however, the differences between the definition of k-apex and Neil Fernandez's definition of k-peak in A101941. - Peter Munn, May 26 2023

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Example

28 is in the sequence because it has two unique prime factors (2 and 7), more than either of its neighbors 27 (one such factor, namely 3) and 29 (one such factor, 29). - Neil Fernandez, Dec 21 2004

Mathematica

omega[n_] := Length[FactorInteger[n]]; Select[Range[3, 500], omega[ # - 1] < omega[ # ] > omega[ # + 1] &]
For[i=1, i<1000, If[And[Length[FactorInteger[i-1]]<Length[FactorInteger[i]], Length[FactorInteger[i+1]]<Length[FactorInteger[i]]], Print[i]]; i++ ] (* Neil Fernandez, Dec 21 2004 *)
#[[2, 1]]&/@Select[Partition[Table[{n, PrimeNu[n]}, {n, 300}], 3, 1], #[[1, 2]]<#[[2, 2]]>#[[3, 2]]&] (* Harvey P. Dale, Dec 11 2011 *)

Prog

(PARI) isok(n) = (omega(n-1) < omega(n)) && (omega(n) > omega(n+1)); \\ Michel Marcus, May 06 2017

Crossrefs

Cf. A001221, A101932, A101941.

Sequence in context: A315130 A315131 A046288 * A064712 A348629 A284667

Adjacent sequences: A076760 A076761 A076762 * A076764 A076765 A076766

Keyword

nonn,easy

Author

Joseph L. Pe, Nov 13 2002

Extensions

Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar

Status

approved