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A076762
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2-apexes of omega: numbers k such that omega(k-2) < omega(k-1) < omega(k) > omega(k+1) > omega(k+2), where omega(m) = the number of distinct prime factors of m.
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1
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105, 165, 195, 315, 345, 399, 465, 1095, 1281, 1305, 1365, 1785, 1995, 2145, 2415, 2475, 2805, 3255, 3465, 3795, 3927, 4515, 4641, 4785, 4935, 5415, 5505, 5565, 5655, 5925, 5985, 6045, 6105, 6195, 6279, 6555, 6699, 6765, 6825, 7215, 7245, 7605, 7725
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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FORMULA
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105 is a term since omega(105) = 3, omega(104) = omgea(106) = 2, and omega(103) = omega(107) = 1, so omega(103) < omega(104) < omega(105) > omega(106) > omega(107).
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MATHEMATICA
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omega[n_] := Length[FactorInteger[n]]; Select[Range[4, 10^4], omega[ # - 2] < omega[ # - 1] < omega[ # ] > omega[ # + 1] > omega[ # + 2] &]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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