A101941 -id:A101941 - cp's OEIS frontend

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

Joseph L. Pe, Nov 13 2002

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

			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

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

Cf. A001221, A101932, A101941.

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 *)

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

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

A101949 Peak-trough transform of the prime-gap sequence (A001223).

Original entry on oeis.org

0, 0, 0, 1, -1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 0, 0, -1, 1, 0, -1, 1, -1, 0, 3, 0, -1, 1, -1, 0, 3, -1, 1, -1, 3, -1, 0, 0, -1, 0, 0, -1, 3, -1, 1, -1, 0, 0, 0, -1, 0, 1, -1, 3, 0, 0, 0, -1, 1, 0, -1, 0, 3, 0, -3, 0, 3, -1, 1, -3, 0, 0

Offset: 1

Neil Fernandez, Dec 22 2004

sign

The peak-trough transform is defined in A101941

			a(4)=1 because A101949(4) is greater than one nearest neighbor on both sides, i.e. A101949(3) and A101949(5), but no more than one.

Cf. A001223, A101941.

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions