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A079615
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Product of all distinct prime factors of all composite numbers between n-th prime and next prime.
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1
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2, 6, 30, 6, 210, 6, 2310, 2730, 30, 39270, 7410, 42, 7590, 46410, 1272810, 30, 930930, 82110, 6, 21111090, 1230, 48969690, 1738215570, 2310, 102, 144690, 6, 85470, 29594505363092670, 16770, 49990710, 138, 7849357706190, 30
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(n) = A007947(A056831(n)), squarefree kernel of least common multiple of composite numbers between n-th prime and next prime.
Note that each term is a product of distinct primes. - T. D. Noe, May 19 2007
Equals A076978 without its first term. [From R. J. Mathar, Sep 19 2008]
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LINKS
| T. D. Noe, Table of n, a(n) for n=2..1000
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EXAMPLE
| 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.
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MATHEMATICA
| 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] (* From Jean-François Alcover, Jul 13 2011 *)
Table[Times@@Union[Flatten[Transpose[FactorInteger[#]][[1]]&/@ (Range[Prime[n]+1, NextPrime[Prime[n]]-1])]], {n, 2, 50}] (* From Harvey P. Dale, Oct 10 2011 *)
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CROSSREFS
| Cf. A005117, A002110.
Sequence in context: A030538 A181812 A076978 * A074168 A117213 A127797
Adjacent sequences: A079612 A079613 A079614 * A079616 A079617 A079618
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KEYWORD
| nonn,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 29 2003
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EXTENSIONS
| Corrected by T. D. Noe, May 19 2007
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