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