

A076778


3nadirs of Omega: numbers k such that Omega(k3) > Omega(k2) > Omega(k1) > 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
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OFFSET

1,1


COMMENTS

I call n a "knadir" (or nadir of depth k) of the arithmetical function f if n satisfies f(nk) > ... > f(n1) > f(n) < f(n+1) < ... < f(n+k).


LINKS



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(n3) gt f(n2) and f(n2) gt f(n1) and f(n1) 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



KEYWORD

nonn


AUTHOR



STATUS

approved



