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A365787
a(n) = A286708(n) divided by its squarefree kernel.
2
6, 12, 10, 18, 24, 14, 20, 36, 15, 48, 54, 28, 40, 72, 21, 22, 50, 96, 108, 45, 26, 56, 80, 144, 30, 44, 162, 100, 33, 75, 192, 34, 35, 216, 63, 52, 98, 38, 39, 112, 160, 288, 42, 60, 88, 324, 200, 135, 46, 384, 68, 250, 432, 51, 90, 104, 196, 76, 486, 55, 147
OFFSET
1,1
COMMENTS
Permutation of numbers that are not prime powers A024619.
LINKS
FORMULA
a(n) = A286708(n)/A007947(A286708(n)) = A286708(n)/A365786(n).
Let b(n) = A286708(n) and let squarefree kernel rad(n) = A007947(n). a(n) >= n such that rad(a(n)) | n.
EXAMPLE
a(1) = 2 since b(1)/rad(b(1)) = 36/6 = 6.
a(2) = 3 since b(2)/rad(b(2)) = 72/6 = 12.
a(3) = 2 since b(3)/rad(b(3)) = 100/10 = 10.
a(4) = 4 since b(4)/rad(b(4)) = 108/6 = 18.
a(5) = 2 since b(5)/rad(b(5)) = 144/6 = 24.
a(6) = 6 since b(6)/rad(b(6)) = 196/14 = 14, etc
MATHEMATICA
nn = 5000;
s = Rest@ Select[Union@ Flatten@
Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
Not @* PrimePowerQ];
t = Select[Range[nn/6], And[SquareFreeQ[#], CompositeQ[#]] &];
Map[FirstPosition[t, Times @@ FactorInteger[#][[All, 1]]][[1]] &, s]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 19 2023
STATUS
approved