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%I #9 Apr 03 2022 11:31:23
%S 1376,6656,9424,12104,18656,19376,29224,30304,40976,41504,41824,44864,
%T 51624,57784,59224,61984,66520,70300,70624,70736,72064,74920,82160,
%U 87296,93500,94424
%N 3-apexes of Omega: numbers k such that Omega(k-3) < Omega(k-2)< Omega(k-1) < Omega(k) > Omega(k+1) > Omega(k+2) > Omega(k+3), where Omega(m) = the number of prime factors of m, counting multiplicity.
%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).
%H Amiram Eldar, <a href="/A076760/b076760.txt">Table of n, a(n) for n = 1..10000</a>
%e Omega(1373) = 1 < Omega(1374) = 3 < Omega(1375) = 4 < Omega(1376)= 6 > Omega(1377) = 5 > Omega(1378) = 3 > Omega(1379) = 2, so 1376 is a 3-apex of Omega.
%t Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Select[Range[5, 10^5], Omega[ # - 3] < Omega[ # - 2] < Omega[ # - 1] < Omega[ # ] > Omega[ # + 1] > Omega[ # + 2] > Omega[ # + 3] &]
%t Flatten[Position[Partition[PrimeOmega[Range[100000]],7,1],_?(#[[1]]< #[[2]]< #[[3]]<#[[4]]>#[[5]]>#[[6]]>#[[7]]&),1,Heads->False]]+3 (* _Harvey P. Dale_, Apr 03 2022 *)
%Y Cf. A001222.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Nov 13 2002
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