A076760 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.

1376, 6656, 9424, 12104, 18656, 19376, 29224, 30304, 40976, 41504, 41824, 44864, 51624, 57784, 59224, 61984, 66520, 70300, 70624, 70736, 72064, 74920, 82160, 87296, 93500, 94424

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

Cf. A001222.

Sequence in context: A206340 A056087 A122692 * A283231 A283790 A345515

Adjacent sequences: A076757 A076758 A076759 * A076761 A076762 A076763

Keyword

nonn

Author

Joseph L. Pe, Nov 13 2002

Status

approved