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

1,2

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.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Formula

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

a(a(n)) = n.

Example

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

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

Prog

(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]))

Crossrefs

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

Sequence in context: A009574 A059422 A102056 * A343130 A065353 A353757

Adjacent sequences: A300952 A300953 A300954 * A300956 A300957 A300958

Keyword

nonn,mult

Author

Rémy Sigrist, Mar 17 2018

Status

approved