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A084371
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Squarefree kernels of powerful numbers (A001694).
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3
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1, 2, 2, 3, 2, 5, 3, 2, 6, 7, 2, 6, 3, 10, 6, 11, 5, 2, 6, 13, 14, 10, 6, 15, 3, 2, 6, 17, 6, 7, 19, 14, 10, 6, 21, 22, 10, 2, 23, 6, 5, 6, 15, 26, 3, 14, 10, 29, 6, 30, 31, 22, 6, 10, 2, 33, 15, 6, 34, 35, 6, 21, 11, 26, 37, 14, 38, 39, 14, 10, 41, 6, 42, 30, 43, 22, 6, 10
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OFFSET
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1,2
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LINKS
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FORMULA
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Sum_{a(k) < x} a(k) = (1/2) * x + o(x) (Jakimczuk, 2017).
Sum_{k=1..n} a(k) ~ c * n^2, where c = (zeta(3)/zeta(3/2))^2/2 = 0.1058641473... . (End)
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EXAMPLE
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A001694(11) = 64 = 2^6 -> a(11) = 2,
A001694(12) = 72 = 2^3 * 3^2 -> a(12) = 2*3 = 6,
A001694(13) = 81 = 3^4 -> a(13) = 3.
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MATHEMATICA
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s = {1}; Do[f = FactorInteger[n]; If[Min @ f[[;; , 2]] > 1, AppendTo[s, Times @@ f[[;; , 1]]]], {n, 2, 10^4}]; s (* Amiram Eldar, Aug 22 2019 *)
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PROG
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(PARI) rad(n) = factorback(factorint(n)[, 1]); \\ A007947
lista(nn) = apply(x->rad(x), select(x->ispowerful(x), [1..nn])); \\ Michel Marcus, Aug 22 2019
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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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