A365793 a(n) = number of k <= b(n) such that rad(k) = rad(b(n)), where rad(n) = A007947(n) and b(n) = A286708(n).

5, 8, 6, 10, 11, 6, 8, 14, 5, 15, 16, 8, 11, 18, 5, 7, 12, 20, 21, 8, 7, 11, 14, 23, 18, 9, 24, 15, 6, 9, 25, 8, 5, 26, 8, 9, 13, 8, 6, 14, 18, 29, 19, 26, 11, 30, 19, 12, 8, 31, 10, 20, 32, 6, 32, 11, 16, 10, 33, 5, 10, 17, 22, 6, 8, 8, 13, 35, 28, 36, 8, 14

Offset: 1

Author

Michael De Vlieger, Sep 22 2023

Keywords

• nonn

Comments

Alternatively, position of A126706(n) in the list k*{R(k)} containing m such that A007947(m) = k, where k = A007947(n).

Examples

			a(1) = 5 since rad(b(1)) = rad(36) = 6, and in the sequence k*{R(6)} = 6*{A003586} = {6, 12, 18, 24, 36, ...}, 36 is the 5th term.
a(2) = 8 since rad(b(2)) = rad(72) = 6, and 72 is the 8th term in k*{R(6)}.
a(3) = 6 since rad(b(3)) = rad(100) = 10, and in the sequence k*{R(10)} = 10*{A003592} = {10, 20, 40, 50, 80, 100, ...}, 100 is the 6th term, etc.
		

Links

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

Crossrefs

Cf. A007947, A286708, A365786, A365792.

Programs

Mathematica

nn = 4000;
f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]];
t = Select[
  Select[Range[nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &],
  AllTrue[FactorInteger[#][[All, -1]], # > 1 &] &];
s = Map[f, t];
Map[Function[k, Set[r[k], k*Select[Range[nn/k], Divisible[k, f[#]] &]]], Union@ s];
Array[FirstPosition[r[s[[#]]], t[[#]]][[1]] &, Length[t]]

Formula

a(n) = A008479(A286708(n)).

a(n) > 1 for all n.