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 A073491 Numbers having no prime gaps in their factorization. 33
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. - R. J. Mathar, Sep 23 2008 The Heinz numbers of the partitions that have no gaps. The Heinz number of a partition p = [p_1, p_2, ..., p_r] is defined as Product_{j=1..r} (p_j-th prime) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). Example: (i) 18 (= 2*3*3) is in the sequence because it is the Heinz number of the partition [1,2,2]; (ii) 10 (= 2*5) is not in the sequence because it is the Heinz number of the partition [1,3]. - Emeric Deutsch, Oct 02 2015 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 EXAMPLE 360 is a term, as 360 = 2*2*2*3*3*5 with consecutive prime factors. MATHEMATICA ok[n_] := (p = FactorInteger[n][[All, 1]]; PrimePi[Last@p] - PrimePi[First@p] == Length[p] - 1); Select[Range, ok] (* Jean-François Alcover, Apr 29 2011 *) npgQ[n_]:=Module[{f=Transpose[FactorInteger[n]][]}, f==Prime[Range[ PrimePi[ f[]], PrimePi[f[[-1]]]]]]; Join[{1}, Select[Range[2, 200], npgQ]] (* Harvey P. Dale, Apr 12 2013 *) PROG (Haskell) a073491 n = a073491_list !! (n-1) a073491_list = filter ((== 0) . a073490) [1..] -- Reinhard Zumkeller, Dec 20 2013 (PARI) is(n)=my(f=factor(n)[, 1]); for(i=2, #f, if(precprime(f[i]-1)>f[i-1], return(0))); 1 \\ Charles R Greathouse IV, Apr 28 2015 CROSSREFS Cf. A137791, A137792, A137793, A137895. Sequence in context: A253784 A251726 A193671 * A066311 A069899 A081306 Adjacent sequences:  A073488 A073489 A073490 * A073492 A073493 A073494 KEYWORD nonn,nice AUTHOR Reinhard Zumkeller, Aug 03 2002 STATUS approved

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Last modified July 18 07:10 EDT 2019. Contains 325134 sequences. (Running on oeis4.)