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

Author

Joseph L. Pe, Nov 13 2002

Keywords

• nonn
• easy

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

Examples

			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
		

Links

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

Crossrefs

Cf. A001221, A101932, A101941.

Programs

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]]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 *)

PARI

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

Extensions

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