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

14, 18, 15, 21, 23, 16, 19, 26, 13, 29, 30, 20, 23, 32, 14, 18, 24, 35, 36, 18, 19, 24, 28, 39, 83, 21, 40, 29, 15, 20, 42, 21, 13, 43, 18, 22, 27, 21, 15, 28, 33, 46, 91, 104, 25, 47, 34, 23, 22, 50, 24, 36, 51, 16, 120, 26, 32, 24, 52, 13, 22, 33, 39, 16, 19

Offset

1,1

Comments

Alternatively, position of A286708(n) in the list R(rad(n)) of k such that rad(k) | n, where rad(n) = A007947(n).

Links

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

Example

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.
a(2) = 18 since rad(b(2)) = rad(72) = 6, and 72 is the 18th term in R(6).
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.

Mathematica

nn = 3300; 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], Select[Range[nn], Divisible[k, f[#]] &]]], Union@ s];
Array[FirstPosition[r[s[[#]]], t[[#]]][[1]] &, Length[t]]

Crossrefs

Cf. A007947, A010846, A286708, A365786, A365793.

Sequence in context: A154146 A113735 A063828 * A060504 A052026 A317743

Adjacent sequences: A365789 A365790 A365791 * A365793 A365794 A365795

Keyword

nonn

Author

Michael De Vlieger, Sep 22 2023

Status

approved