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A075366
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Smallest product (n+1)(n+2)...(n+k) that is divisible by the product of all the primes up to n.
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3
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1, 12, 120, 30, 30240, 5040, 17297280, 2162160, 240240, 360360, 28158588057600, 2346549004800, 64764752532480000, 4626053752320000, 308403583488000, 19275223968000, 830034394580628357120000, 46113021921146019840000
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..18.
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FORMULA
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If p <= n < q, where p and q are consecutive primes, then a(n) = (2p)!/n!, unless n=10.
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MATHEMATICA
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a75365[n_] := Module[{div, k, pr}, div=Times@@Prime/@Range[PrimePi[n]]; For[k=0; pr=1, True, k++; pr*=n+k, If[Mod[pr, div]==0, Return[k]]]]; a[n_] := Times@@Range[n+1, n+a75365[n]]
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CROSSREFS
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Cf. A075365, A075367, A075368.
Sequence in context: A077251 A075622 A153054 * A076633 A110423 A006953
Adjacent sequences: A075363 A075364 A075365 * A075367 A075368 A075369
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KEYWORD
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nice,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 20 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Oct 28 2002
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STATUS
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approved
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