A076761 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 distinct prime factors of m.

104006, 272986, 557480, 706706, 757316, 835016, 908600, 948310, 995554, 1093730, 1181410, 1198406, 1212694, 1252510, 1253330, 1283710, 1352560, 1370915, 1428686, 1440880, 1452836, 1513730, 1524446, 1627444, 1654730, 1662310

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(104003), ..., omega(104006), ..., omega(104009) equal 1, 3, 4, 5, 3, 2, 1, respectively. Hence 104006 is a term of the sequence.

Mathematica

omega[n_] := Length[FactorInteger[n]]; Select[Range[5, 10^6], omega[ # - 3] < omega[ # - 2] < omega[ # - 1] < omega[ # ] > omega[ # + 1] > omega[ # + 2] > omega[ # + 3] &]
okQ[{a_, b_, c_, d_, e_, f_, g_}]:=a<b<c<d>e>f>g; Flatten[ Position[ Partition[ PrimeNu[ Range[167*10^4]], 7, 1], _?(okQ[#]&)]]+3 (* Harvey P. Dale, Jul 27 2019 *)

Prog

(Magma) pd:=PrimeDivisors; f:=func<n|#pd(n-3) lt #pd(n-2) and #pd(n-2) lt #pd(n-1) and #pd(n-1) lt #pd(n)>; f1:=func<n|#pd(n) gt #pd(n+1) and #pd(n+1) gt #pd(n+2) and #pd(n+2) gt #pd(n+3)>; [k:k in [4..170000]|f(k) and f1(k)]; // Marius A. Burtea, Feb 18 2020

Crossrefs

Cf. A001222.

Sequence in context: A210180 A136312 A205260 * A236007 A129241 A290535

Adjacent sequences: A076758 A076759 A076760 * A076762 A076763 A076764

Keyword

nonn

Author

Joseph L. Pe, Nov 13 2002

Extensions

a(10)-a(26) from Donovan Johnson, Feb 07 2009

Status

approved