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.

189, 315, 405, 675, 729, 891, 1029, 1053, 1269, 1376, 1395, 1485, 1683, 1701, 1755, 1845, 1863, 1875, 1917, 1995, 2025, 2205, 2349, 2457, 2475, 2691, 2709, 2805, 2835, 2925, 2997, 3003, 3075, 3125, 3267, 3315, 3375, 3465, 3525, 3576, 3591, 3675, 3861

Offset: 1

Author

Joseph L. Pe, Nov 13 2002

Keywords

• nonn

Comments

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).

Examples

			Omega(187) = 2 < Omega(188) = 3 < Omega(189) = 4 > Omega(190)= 3 > Omega(191) = 1, so 189 is a 2-apex of Omega.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001222.

Programs

Mathematica

Select[Range[4, 10^4], Omega[ # - 2] < Omega[ # - 1] < Omega[ # ] > Omega[ # + 1] > Omega[ # + 2] &]
Flatten[Position[Partition[PrimeOmega[Range[4000]],5,1],?(#[[1]]<#[[2]]<#[[3]]> #[[4]]> #[[5]]&),1,Heads->False]]+2 (* _Harvey P. Dale, Apr 11 2022 *)