cp's OEIS Frontend

A076759 2-apexes of Omega: numbers k such that Omega(k-2)< Omega(k-1) < Omega(k) > Omega(k+1) > Omega(k+2), where Omega(m) = the number of prime factors of m, counting multiplicity.

%I A076759 #9 Apr 11 2022 17:47:38
%S A076759 189,315,405,675,729,891,1029,1053,1269,1376,1395,1485,1683,1701,1755,
%T A076759 1845,1863,1875,1917,1995,2025,2205,2349,2457,2475,2691,2709,2805,
%U A076759 2835,2925,2997,3003,3075,3125,3267,3315,3375,3465,3525,3576,3591,3675,3861
%N A076759 2-apexes of Omega: numbers k such that Omega(k-2)< Omega(k-1) < Omega(k) > Omega(k+1) > Omega(k+2), where Omega(m) = the number of prime factors of m, counting multiplicity.
%C A076759 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 A076759 Amiram Eldar, <a href="/A076759/b076759.txt">Table of n, a(n) for n = 1..10000</a>
%e A076759 Omega(187) = 2 < Omega(188) = 3 < Omega(189) = 4 > Omega(190)= 3 > Omega(191) = 1, so 189 is a 2-apex of Omega.
%t A076759 Select[Range[4, 10^4], Omega[ # - 2] < Omega[ # - 1] < Omega[ # ] > Omega[ # + 1] > Omega[ # + 2] &]
%t A076759 Flatten[Position[Partition[PrimeOmega[Range[4000]],5,1],_?(#[[1]]<#[[2]]<#[[3]]> #[[4]]> #[[5]]&),1,Heads->False]]+2 (* _Harvey P. Dale_, Apr 11 2022 *)
%Y A076759 Cf. A001222.
%K A076759 nonn
%O A076759 1,1
%A A076759 _Joseph L. Pe_, Nov 13 2002