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A076760 3-apexes of Omega: n such that Omega(n-3) < Omega(n-2)< Omega(n-1) < Omega(n) > Omega(n+1) > Omega(n+2) > Omega(n+3), where Omega(m) = the number of prime factors of m, counting multiplicity. 0

%I

%S 1376,6656,9424,12104,18656,19376,29224,30304,40976,41504,41824,44864,

%T 51624,57784,59224,61984,66520,70300,70624,70736,72064,74920,82160,

%U 87296,93500,94424

%N 3-apexes of Omega: n such that Omega(n-3) < Omega(n-2)< Omega(n-1) < Omega(n) > Omega(n+1) > Omega(n+2) > Omega(n+3), where Omega(m) = the number of prime factors of m, counting multiplicity.

%C 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).

%e 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.

%t 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] &]

%Y Cf. A001222.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Nov 13 2002

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)