|
%I #10 Sep 20 2023 12:21:08
%S 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,
%T 10,33,15,6,34,35,6,21,26,14,38,39,14,10,6,42,30,22,6,10,15,46,6,34,
%U 10,6,51,30,26,14,38,6,55,21,14,10,57,33,58,15,6,42,30,62
%N a(n) = squarefree kernel of A286708(n).
%C Terms are squarefree and composite, i.e., in A120944.
%H Michael De Vlieger, <a href="/A365786/b365786.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A007947(A286708(n)).
%e Let b(n) = A286708(n) and let squarefree kernel rad(n) = A007947(n).
%e a(1) = 6 = rad(b(1)) = rad(36).
%e a(2) = 6 = rad(b(2)) = rad(72).
%e a(3) = 10 = rad(b(3)) = rad(100), etc.
%t 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]] ]
%o (PARI) apply(x->factorback(factorint(x)[, 1]), select(x->((x>1) && ispowerful(x) && !isprimepower(x)), [1..5000])) \\ _Michel Marcus_, Sep 20 2023
%Y Cf. A001694, A007947, A084371, A120944, A126706, A286708.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Sep 19 2023
|
