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 A097889 Numbers that are products of (at least two) consecutive primes. 10
 6, 15, 30, 35, 77, 105, 143, 210, 221, 323, 385, 437, 667, 899, 1001, 1147, 1155, 1517, 1763, 2021, 2310, 2431, 2491, 3127, 3599, 4087, 4199, 4757, 5005, 5183, 5767, 6557, 7387, 7429, 8633, 9797, 10403, 11021, 11663, 12317, 12673, 14351, 15015, 16637, 17017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Subsequence of A073485; A073490(a(n)) = 0. - Reinhard Zumkeller, Nov 20 2004 A proper subset of A073485. - Robert G. Wilson v, Jun 11 2010 a(A192280(n)) * (1 - A010051(a(n)) = 1. The Heinz numbers of the partitions into at least 2 consecutive parts. The Heinz number of an integer partition p = [p_1, p_2, ..., p_r] is defined as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). Examples: (i) 105 (=3*5*7) is in the sequence because it is the Heinz number of the partition [2,3,4]; (ii) 108 (= 2*2*3*3*3) is not in the sequence because it is the Heinz number of the partition [1,1,2,2,2]. - Emeric Deutsch, Oct 02 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) ~ n^2 log^2 n. - Charles R Greathouse IV, Oct 24 2012 EXAMPLE 1001 = 7 * 11 * 13. MAPLE isA097889 := proc(n)     local plist, p, i ;     plist := sort(convert(numtheory[factorset](n), list)) ;     if nops(plist) < 2 then         return false;     end if;     for i from 1 to nops(plist) do         p := op(i, plist) ;         if modp(n, p^2) = 0 then             return false;         end if;         if i > 1 then             if nextprime(op(i-1, plist)) <> p then                 return false;             end if;         end if;     end do:     true; end proc: for n from 1 to 1000 do     if isA097889(n) then         printf("%d, ", n);     end if; end do: # R. J. Mathar, Jan 12 2016 MATHEMATICA a = {}; Do[ AppendTo[a, Apply[ Times, (Prime /@ Partition[ Range[30], n, i]), 1]], {n, 2, 6}, {i, n - 1}]; Take[ Union[ Flatten[ a]], 45] (* Robert G. Wilson v, Sep 24 2004 *) PROG (Haskell) import Data.Set (singleton, deleteFindMin, insert) a097889 n = a097889_list !! (n-1) a097889_list = f \$ singleton (6, 2, 3) where    f s = y : f (insert (w, p, q') \$ insert (w `div` p, a151800 p, q') s')          where w = y * q'; q' = a151800 q                ((y, p, q), s') = deleteFindMin s -- Reinhard Zumkeller, May 12 2015, Aug 26 2011 (PARI) list(lim)=my(v=List(), p, t); for(e=2, log(lim+.5)\log(2), p=1; t=prod(i=1, e-1, prime(i)); forprime(q=prime(e), lim, t*=q/p; if(t>lim, next(2)); listput(v, t); p=nextprime(p+1))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Oct 24 2012 CROSSREFS Union of A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, etc. Cf. A050936. Intersection of A073485 and A002808. Cf. A151800, A215366. Sequence in context: A024972 A048749 A336905 * A256874 A250121 A024802 Adjacent sequences:  A097886 A097887 A097888 * A097890 A097891 A097892 KEYWORD nonn,easy AUTHOR Bart la Bastide (bart(AT)xs4all.nl), Sep 21 2004 EXTENSIONS More terms from Robert G. Wilson v, Sep 24 2004 Data corrected for n > 41 by Reinhard Zumkeller, Aug 26 2011 STATUS approved

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Last modified September 20 20:02 EDT 2020. Contains 337265 sequences. (Running on oeis4.)