login
A365789
Position of A365787(n) in A024619.
1
1, 3, 2, 6, 10, 4, 7, 17, 5, 25, 29, 12, 20, 42, 8, 9, 26, 61, 69, 23, 11, 31, 48, 96, 13, 22, 111, 64, 14, 44, 134, 15, 16, 154, 36, 28, 62, 18, 19, 72, 109, 210, 21, 34, 54, 240, 139, 89, 24, 288, 39, 181, 329, 27, 55, 66, 137, 45, 374, 30, 99, 161, 236, 32
OFFSET
1,2
COMMENTS
Permutation of natural numbers.
EXAMPLE
Let b(n) = A286708(n), rad(n) = A007947(n), and c(n) = A024619(n).
a(1) = 1 since b(1)/rad(b(1)) = 36/6 = 6 = c(1).
a(2) = 3 since b(2)/rad(b(2)) = 72/6 = 12 = c(3).
a(3) = 2 since b(3)/rad(b(3)) = 100/10 = 10 = c(2).
a(4) = 6 since b(4)/rad(b(4)) = 108/6 = 18 = c(6).
a(5) = 10 since b(5)/rad(b(5)) = 144/6 = 24 = c(10).
a(6) = 4 since b(6)/rad(b(6)) = 196/14 = 14 = c(4), etc.
MATHEMATICA
nn = 3600;
s = Rest@
Select[Union@ Flatten@
Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}],
Not @* PrimePowerQ];
t = Select[Range[2, nn], Not @* PrimePowerQ];
Map[FirstPosition[t, #/(Times @@ FactorInteger[#][[All, 1]])][[1]] &, s]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 19 2023
STATUS
approved