Michael De Vlieger, <a href="/A365786/b365786_1.txt">Table of n, a(n) for n = 1..10000</a>

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OEIS Server: Installed first b-file as b365786.txt.

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Michel Marcus: oh sorry

(PARI) apply(x->factorback(factorint(x)[, 1]), select(x->((x>1) && ispowerful(x) && !isprimepower(x)), [1..5000])) \\ Michel Marcus, Sep 20 2023

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reviewed

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Michael De Vlieger, <a href="/A365786/b365786_1.txt">Table of n, a(n) for n = 1..10000</a>

allocated for Michael De Vlieger

a(n) = squarefree kernel of A286708(n).

6, 6, 10, 6, 6, 14, 10, 6, 15, 6, 6, 14, 10, 6, 21, 22, 10, 6, 6, 15, 26, 14, 10, 6, 30, 22, 6, 10, 33, 15, 6, 34, 35, 6, 21, 26, 14, 38, 39, 14, 10, 6, 42, 30, 22, 6, 10, 15, 46, 6, 34, 10, 6, 51, 30, 26, 14, 38, 6, 55, 21, 14, 10, 57, 33, 58, 15, 6, 42, 30, 62

1,1

Terms are squarefree and composite, i.e., in A120944.

a(n) = A007947(A286708(n)).

Let b(n) = A286708(n) and let squarefree kernel rad(n) = A007947(n).

a(1) = 6 = rad(b(1)) = rad(36).

a(2) = 6 = rad(b(2)) = rad(72).

a(3) = 10 = rad(b(3)) = rad(100), etc.

With[{nn = 2^12}, Map[Times @@ FactorInteger[#][[All, 1]] &, Rest@ Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], Not @* PrimePowerQ]] ]

Cf. A001694, A007947, A084371, A120944, A126706, A286708.

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Michael De Vlieger, Sep 19 2023

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editing

allocated for Michael De Vlieger

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