login
A365786
a(n) = squarefree kernel of A286708(n).
5
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
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
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 19 2023
STATUS
approved