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A073491
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Numbers having no prime gaps in their factorization.
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24
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1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 23, 24, 25, 27, 29, 30, 31, 32, 35, 36, 37, 41, 43, 45, 47, 48, 49, 53, 54, 59, 60, 61, 64, 67, 71, 72, 73, 75, 77, 79, 81, 83, 89, 90, 96, 97, 101, 103, 105, 107, 108, 109, 113, 120, 121, 125, 127, 128, 131, 135
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OFFSET
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1,2
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COMMENTS
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A073490(a(n)) = 0; subsequences are: A000040, A000961, A006094, A002110, A000142, A073485.
A137721(n) = number of terms not greater than n; A137794(a(n))=1; complement of A073492. - Reinhard Zumkeller, Feb 11 2008
Essentially the same as A066311. [From R. J. Mathar, Sep 23 2008]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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EXAMPLE
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360 is a term, as 360 = 2*2*2*3*3*5 with consecutive prime factors.
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MATHEMATICA
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ok[n_] := (p = FactorInteger[n][[All, 1]]; PrimePi[Last@p] - PrimePi[First@p] == Length[p] - 1); Select[Range[135], ok] (* From Jean-François Alcover, Apr 29 2011 *)
npgQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]}, f==Prime[Range[ PrimePi[ f[[1]]], PrimePi[f[[-1]]]]]]; Join[{1}, Select[Range[2, 200], npgQ]] (* Harvey P. Dale, Apr 12 2013 *)
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CROSSREFS
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Cf. A137791, A137792, A137793.
Cf. A137895.
Sequence in context: A074779 A048197 A193671 * A066311 A069899 A081306
Adjacent sequences: A073488 A073489 A073490 * A073492 A073493 A073494
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KEYWORD
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nonn,nice
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AUTHOR
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Reinhard Zumkeller, Aug 03 2002
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STATUS
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approved
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