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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.

%I A076763 #20 May 26 2023 11:29:39
%S A076763 6,10,12,18,24,26,28,30,42,48,60,66,70,72,78,80,82,84,90,102,105,108,
%T A076763 110,114,120,126,130,132,138,140,150,154,156,165,168,170,174,180,182,
%U A076763 186,190,192,195,198,204,210,220,222,228,234,238,240,242,246,252,255
%N 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.
%C A076763 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).
%C A076763 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
%H A076763 G. C. Greubel, <a href="/A076763/b076763.txt">Table of n, a(n) for n = 1..5000</a>
%e A076763 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
%t A076763 omega[n_] := Length[FactorInteger[n]]; Select[Range[3, 500], omega[ # - 1] < omega[ # ] > omega[ # + 1] &]
%t A076763 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 *)
%t A076763 #[[2,1]]&/@Select[Partition[Table[{n,PrimeNu[n]},{n,300}],3,1],#[[1,2]]<#[[2,2]]>#[[3,2]]&] (* _Harvey P. Dale_, Dec 11 2011 *)
%o A076763 (PARI) isok(n) = (omega(n-1) < omega(n)) && (omega(n) > omega(n+1)); \\ _Michel Marcus_, May 06 2017
%Y A076763 Cf. A001221, A101932, A101941.
%K A076763 nonn,easy
%O A076763 1,1
%A A076763 _Joseph L. Pe_, Nov 13 2002
%E A076763 Edited by _N. J. A. Sloane_, Sep 06 2008 at the suggestion of _R. J. Mathar_