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A365792 a(n) = number of k <= b(n) such that rad(k) | b(n), where rad(n) = A007947(n) and b(n) = A286708(n).

%I A365792 #9 Oct 22 2023 01:25:08
%S A365792 14,18,15,21,23,16,19,26,13,29,30,20,23,32,14,18,24,35,36,18,19,24,28,
%T A365792 39,83,21,40,29,15,20,42,21,13,43,18,22,27,21,15,28,33,46,91,104,25,
%U A365792 47,34,23,22,50,24,36,51,16,120,26,32,24,52,13,22,33,39,16,19
%N A365792 a(n) = number of k <= b(n) such that rad(k) | b(n), where rad(n) = A007947(n) and b(n) = A286708(n).
%C A365792 Alternatively, position of A286708(n) in the list R(rad(n)) of k such that rad(k) | n, where rad(n) = A007947(n).
%H A365792 Michael De Vlieger, <a href="/A365792/b365792.txt">Table of n, a(n) for n = 1..10000</a>
%e A365792 a(1) = 14 since rad(b(1)) = rad(36) = 6, and in the sequence R(6) = A003586 = {1, 2, 3, 4, 6, 8, 9, ..., 36, ...}, 36 is the 14th term.
%e A365792 a(2) = 18 since rad(b(2)) = rad(72) = 6, and 72 is the 18th term in R(6).
%e A365792 a(3) = 15 since rad(b(3)) = rad(100) = 10, and in the sequence R(10) = A003592 = {1, 2, 4, 5, 8, 10, ..., 100, ...}, 100 is the 15th term, etc.
%t A365792 nn = 3300; f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]];
%t A365792 t = Select[
%t A365792   Select[Range[nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &],
%t A365792   AllTrue[FactorInteger[#][[All, -1]], # > 1 &] &];
%t A365792 s = Map[f, t];
%t A365792 Map[Function[k, Set[r[k], Select[Range[nn], Divisible[k, f[#]] &]]], Union@ s];
%t A365792 Array[FirstPosition[r[s[[#]]], t[[#]]][[1]] &, Length[t]]
%Y A365792 Cf. A007947, A010846, A286708, A365786, A365793.
%K A365792 nonn
%O A365792 1,1
%A A365792 _Michael De Vlieger_, Sep 22 2023