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A300955
In the prime tower factorization of n, replace 2's with 3's and 3's with 2's.
4
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.
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
KEYWORD
nonn,mult
AUTHOR
Rémy Sigrist, Mar 17 2018
STATUS
approved