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
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
KEYWORD
nonn,mult
AUTHOR
Rémy Sigrist, Mar 17 2018
STATUS
approved