A300955 In the prime tower factorization of n, replace 2's with 3's and 3's with 2's.

1, 3, 2, 27, 5, 6, 7, 9, 8, 15, 11, 54, 13, 21, 10, 7625597484987, 17, 24, 19, 135, 14, 33, 23, 18, 125, 39, 4, 189, 29, 30, 31, 243, 22, 51, 35, 216, 37, 57, 26, 45, 41, 42, 43, 297, 40, 69, 47, 15251194969974, 343, 375, 34, 351, 53, 12, 55, 63, 38, 87, 59

Offset: 1

Author

Rémy Sigrist, Mar 17 2018

Keywords

• nonn
• mult

Comments

The prime tower factorization of a number is defined in A182318.

This sequence is a self-inverse multiplicative permutation of the natural numbers.

This sequence has infinitely many fixed points (A300957); for any k > 0, at least one of k or 2^k * 3^a(k) is a fixed point.

This sequence is a recursive version of A182318.

This sequence has connections with A300948.

Examples

			a(6) = a(2 * 3) = 3 * 2 = 6.
a(16) = a(2 ^ 2 ^ 2) = 3 ^ 3 ^ 3 = 7625597484987.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A064614, A182318, A300948, A300957 (fixed points).

Programs

Maple

a:= n-> `if`(n=1, 1, mul(`if`(i[1]=2, 3, `if`(i[1]=3,
             2, i[1]))^a(i[2]), i=ifactors(n)[2])):
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 17 2018

Mathematica

a[n_] := If[n == 1, 1, Product[If[i[[1]] == 2, 3, If[i[[1]] == 3,
   2, i[[1]]]]^a[i[[2]]], {i, FactorInteger[n]}]];
Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Jan 30 2025, after Alois P. Heinz *)

PARI

a(n) = my (f=factor(n)); prod(i=1, #f~, my (p=f[i,1]); if (p==2, 3, p==3, 2, p)^a(f[i,2]))

Formula

Multiplicative with a(p^k) = A064614(p)^a(k).

a(a(n)) = n.