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A276152
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a(n) = {smallest prime not dividing n} times {greatest primorial number which divides n} = A053669(n) * A053589(n).
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6
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2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 210, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 210, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 210, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6, 2, 6, 2, 30, 2, 6
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OFFSET
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1,1
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COMMENTS
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a(n) with n odd must = 2 because 1 is the only odd primorial, thereby the only primorial dividing odd n, and 2 is the smallest prime not dividing odd n. - Michael De Vlieger, Aug 25 2016
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LINKS
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FORMULA
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EXAMPLE
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a(6) = 30 because the smallest nondivisor prime 6 = 5 and the smallest primorial dividing 6 is 6 itself. 5 * 6 = 30.
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MATHEMATICA
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Table[If[n == 1, 2, Prime@If[! MemberQ[#, 0], Length@ # + 1, Position[#, 0][[1, 1]]] (Times @@ Prime@ Flatten@ Position[TakeWhile[#, # > 0 &], 1]) &@ Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@# -> 1 &, f]]@ FactorInteger@ n], {n, 120}] (* or *)
Table[If[OddQ@ n, 2, Function[p, Prime[p + 1] Product[Prime@ k, {k, #[[p]]}]][LengthWhile[Differences@ #, # == 1 &] + 1] &@ PrimePi[FactorInteger[n][[All, 1]]]], {n, 120}] (* Michael De Vlieger, Aug 25 2016 *)
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PROG
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(Scheme, two versions)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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