A348018 a(n) is the index of A064549(n) = n * Product_{p prime|n} p in the sequence of powerful numbers (A001694).

1, 2, 4, 3, 6, 9, 10, 5, 7, 14, 16, 12, 20, 21, 24, 8, 28, 15, 31, 22, 35, 36, 39, 19, 17, 44, 13, 32, 48, 50, 51, 11, 56, 59, 60, 23, 65, 67, 68, 33, 71, 73, 75, 52, 43, 81, 84, 27, 30, 37, 90, 64, 94, 29, 97, 46, 102, 104, 107, 74, 110, 111, 62, 18, 117, 119

Offset: 1

Author

Amiram Eldar, Sep 24 2021

Keywords

• nonn

Comments

A permutation of the positive integers.

The inverse permutation of A306458.

Examples

			The sequence of powerful numbers (A001694) begins with 1, 4, 8, 9, ...
The position of A064549(1) = 1 in A001694 is 1, so a(1) = 1.
The position of A064549(3) = 9 in A001694 is 4, so a(3) = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001694, A064549, A306458.

Programs

Mathematica

powQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # > 1 &]; pows = Join[{1}, Select[Range[10^4], powQ]]; TakeWhile[Table[FirstPosition[pows, n * Times @@ (First /@ FactorInteger[n])][[1]], {n, 1, 100}], NumericQ]

Formula

A001694(a(n)) = A064549(n).

A306458(a(n)) = a(A306458(n)) = n.

The fixed points of this permutation are 1, 2, 12, 1208, 1256, 1288 and no more below 3*10^5.