OFFSET
1,1
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).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
MATHEMATICA
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] &]
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Nov 13 2002
STATUS
approved