A365786 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

Offset

1,1

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

Mathematica

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]] ]

Prog

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

Crossrefs

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

Sequence in context: A291545 A205372 A301690 * A365783 A366937 A096474

Adjacent sequences: A365783 A365784 A365785 * A365787 A365788 A365789

Keyword

nonn

Author

Michael De Vlieger, Sep 19 2023

Status

approved