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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)