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%I #30 Jun 01 2020 12:49:58
%S 2,6,30,6,210,6,2310,2730,30,39270,7410,42,7590,46410,1272810,30,
%T 930930,82110,6,21111090,1230,48969690,1738215570,2310,102,144690,6,
%U 85470,29594505363092670,16770,49990710,138,7849357706190,30
%N Product of all distinct prime factors of all composite numbers between n-th prime and next prime.
%C a(n) = A007947(A056831(n)), squarefree kernel of least common multiple of composite numbers between n-th prime and next prime.
%C Note that each term is a product of distinct primes. - _T. D. Noe_, May 19 2007
%C Equals A076978 without its first term. - _R. J. Mathar_, Sep 19 2008
%C Same for A074168. - _Georg Fischer_, Oct 06 2018
%C For n > 2, a(n) is of the form 2*3*r, where r is relatively prime to 6. Therefore, for every n > 2, a(n) is a Zumkeller number (see Corollary 5, Rao/Peng link). - _Ivan N. Ianakiev_, Jan 24 2020
%H T. D. Noe, <a href="/A079615/b079615.txt">Table of n, a(n) for n = 2..1000</a>
%H K. P. S. Bhaskara Rao and Yuejian Peng, <a href="https://doi.org/10.1016/j.jnt.2012.09.020">On Zumkeller Numbers</a>, Journal of Number Theory, Volume 133, Issue 4, April 2013, pp. 1135-1155.
%e n=9: factorizations of numbers between 23=A000040(9) and 29=A000040(10) are 24=3*2^3, 25=5^2, 26=13*2 and 27=3^3, therefore a(9) = 2*3*5*7*13 = 2730.
%t a[n_] := (p = Prime[n]; s = Select[Table[k, {k, p, NextPrime[p]}], ! PrimeQ[#] &]; Times @@ ((FactorInteger /@ s // Flatten[#, 1] &)[[All, 1]] // Union)); a /@ Range[2, 35] (* _Jean-François Alcover_, Jul 13 2011 *)
%t Table[Times@@Union[Flatten[Transpose[FactorInteger[#]][[1]]&/@ (Range[ Prime[ n]+1, NextPrime[Prime[n]]-1])]],{n,2,50}] (* _Harvey P. Dale_, Oct 10 2011 *)
%Y Cf. A005117, A002110, A083207.
%K nonn,nice
%O 2,1
%A _Reinhard Zumkeller_, Jan 29 2003
%E Corrected by _T. D. Noe_, May 19 2007
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