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A070077
Greatest common divisor of n-th squarefree number and n-th cubefree number.
2
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
OFFSET
1,2
COMMENTS
a(n) is squarefree.
Conjecture: for any squarefree k exists m such that a(m)=k; see A070078.
LINKS
Eric Weisstein's World of Mathematics, Cubefree.
Eric Weisstein's World of Mathematics, Squarefree.
FORMULA
a(n) = GCD(A005117(n), A004709(n)).
EXAMPLE
a(10) = GCD(A005117(10), A004709(10)) = GCD(14,11) = 1.
a(11) = GCD(A005117(11), A004709(11)) = GCD(15,12) = 3*GCD(5,4) = 3*1 = 3.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 22 2002
STATUS
approved