A076778 3-nadirs 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(k) = number of prime factors of k, counting multiplicity.

40147, 126173, 168907, 230947, 255427, 322627, 383133, 393027, 393773, 415677, 450173, 466827, 495123, 502973, 579533, 661747, 692547, 745747, 757227, 777773, 803157, 816573, 824947, 846173, 863453, 902333, 919389, 942653, 946013, 959213

Offset

1,1

Comments

I call n a "k-nadir" (or nadir of depth 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

Mathematica

Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Select[Range[5, 10^6], Omega[ # - 3] > Omega[ # - 2] > Omega[ # - 1] > Omega[ # ] < Omega[ # + 1] < Omega[ # + 2] < Omega[ # + 3] &]

Prog

(Magma) f:=func<n|&+[p[2]: p in Factorization(n)]>; f1:=func<n| f(n-3) gt f(n-2) and f(n-2) gt f(n-1)  and f(n-1) gt f(n)  >;  f2:=func<n| f(n+3) gt f(n+2) and f(n+2) gt f(n+1)  and f(n+1) gt f(n)  >; [k:k in [5..960000]| f1(k) and f2(k)]; // Marius A. Burtea, Feb 19 2020

Crossrefs

Cf. A001222.

Sequence in context: A250079 A237238 A236253 * A172863 A159720 A127228

Adjacent sequences: A076775 A076776 A076777 * A076779 A076780 A076781

Keyword

nonn

Author

Joseph L. Pe, Nov 14 2002

Status

approved