

A076763


1apexes of omega: numbers n such that omega(n1) < omega(n) > omega(n+1), where omega(m) = the number of distinct prime factors of m.


5



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
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OFFSET

1,1


COMMENTS

I call n a "kapex" (or "apex of height k") of the arithmetical function f if n satisfies f(nk) < ... < f(n1) < f(n) > f(n+1) > .... > f(n+k).


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[i1]]<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(n1) < omega(n)) && (omega(n) > omega(n+1)); \\ Michel Marcus, May 06 2017


CROSSREFS

Cf. A101932, A001221.
Sequence in context: A315130 A315131 A046288 * A064712 A284667 A315132
Adjacent sequences: A076760 A076761 A076762 * A076764 A076765 A076766


KEYWORD

nonn


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



