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A076763
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1-apexes of omega: numbers n such that omega(n-1) < omega(n) > omega(n+1), where omega(m) = the number of distinct prime factors of m.
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4
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6, 10, 12, 18, 24, 26, 28, 30, 42, 48, 60, 66, 70, 72, 78, 80, 82, 84, 90, 102, 105, 108, 110, 114, 120, 126, 130, 132, 138, 140, 150, 154, 156, 165, 168, 170, 174, 180, 182, 186, 190, 192, 195, 198, 204, 210, 220, 222, 228, 234, 238, 240, 242, 246, 252, 255
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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EXAMPLE
| 28 is in the sequence because it has two unique prime factors (2 and 7), more than either of its neighbors 27 (one such factor, namely 3) and 29 (one such factor, 29). - N. Fernandez (primeness(AT)borve.org), Dec 21 2004
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MATHEMATICA
| omega[n_] := Length[FactorInteger[n]]; Select[Range[3, 500], omega[ # - 1] < omega[ # ] > omega[ # + 1] &]
For[i=1, i<1000, If[And[Length[FactorInteger[i-1]]<Length[FactorInteger[i]], Length[FactorInteger[i+1]]<Length[FactorInteger[i]]], Print[i]]; i++ ] - N. Fernandez (primeness(AT)borve.org), Dec 21 2004
#[[2, 1]]&/@Select[Partition[Table[{n, PrimeNu[n]}, {n, 300}], 3, 1], #[[1, 2]]<#[[2, 2]]>#[[3, 2]]&] (* From Harvey P. Dale, Dec 11 2011 *)
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CROSSREFS
| Cf. A101932, A001221.
Sequence in context: A110085 A114520 A046288 * A064712 A098669 A046363
Adjacent sequences: A076760 A076761 A076762 * A076764 A076765 A076766
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Nov 13 2002
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2008 at the suggestion of R. J. Mathar
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