cp's OEIS Frontend

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).

%I A365793 #6 Oct 06 2023 11:10:37
%S A365793 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,
%T A365793 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,
%U A365793 6,32,11,16,10,33,5,10,17,22,6,8,8,13,35,28,36,8,14
%N 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).
%C A365793 Alternatively, position of A126706(n) in the list k*{R(k)} containing m such that A007947(m) = k, where k = A007947(n).
%H A365793 Michael De Vlieger, <a href="/A365793/b365793.txt">Table of n, a(n) for n = 1..10000</a>
%F A365793 a(n) = A008479(A286708(n)).
%F A365793 a(n) > 1 for all n.
%e A365793 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.
%e A365793 a(2) = 8 since rad(b(2)) = rad(72) = 6, and 72 is the 8th term in k*{R(6)}.
%e A365793 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.
%t A365793 nn = 4000;
%t A365793 f[x_] := f[x] = Times @@ FactorInteger[x][[All, 1]];
%t A365793 t = Select[
%t A365793   Select[Range[nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &],
%t A365793   AllTrue[FactorInteger[#][[All, -1]], # > 1 &] &];
%t A365793 s = Map[f, t];
%t A365793 Map[Function[k, Set[r[k], k*Select[Range[nn/k], Divisible[k, f[#]] &]]], Union@ s];
%t A365793 Array[FirstPosition[r[s[[#]]], t[[#]]][[1]] &, Length[t]]
%Y A365793 Cf. A007947, A286708, A365786, A365792.
%K A365793 nonn
%O A365793 1,1
%A A365793 _Michael De Vlieger_, Sep 22 2023