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A070077
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Greatest common divisor of n-th squarefree number and n-th cubefree number.
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2
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1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 1
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OFFSET
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1,2
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COMMENTS
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a(n) is squarefree.
Conjecture: for any squarefree k exists m such that a(m)=k; see A070078.
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LINKS
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Eric Weisstein's World of Mathematics, Cubefree.
Eric Weisstein's World of Mathematics, Squarefree.
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FORMULA
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EXAMPLE
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a(11) = GCD(A005117(11), A004709(11)) = GCD(15,12) = 3*GCD(5,4) = 3*1 = 3.
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MATHEMATICA
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With[{max = 150}, e = Max[FactorInteger[#][[;; , 2]]] & /@ Range[max]; sqf = Flatten[Position[e, _?(# < 2 &)]]; cbf = Flatten[Position[e, _?(# < 3 &)]]; GCD[sqf, cbf[[1 ;; Length[sqf]]]]] (* Amiram Eldar, Oct 20 2023 *)
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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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