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

1,2

Comments

A permutation of the positive integers.

The inverse permutation of A306458.

Links

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

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.

Example

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.

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]

Crossrefs

Cf. A001694, A064549, A306458.

Sequence in context: A095167 A075383 A338919 * A363504 A332878 A113233

Adjacent sequences: A348015 A348016 A348017 * A348019 A348020 A348021

Keyword

nonn

Author

Amiram Eldar, Sep 24 2021

Status

approved