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A064614
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Exchange 2 and 3 in the prime factorization of n.
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5
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1, 3, 2, 9, 5, 6, 7, 27, 4, 15, 11, 18, 13, 21, 10, 81, 17, 12, 19, 45, 14, 33, 23, 54, 25, 39, 8, 63, 29, 30, 31, 243, 22, 51, 35, 36, 37, 57, 26, 135, 41, 42, 43, 99, 20, 69, 47, 162, 49, 75, 34, 117, 53, 24, 55, 189, 38, 87, 59, 90, 61, 93, 28, 729, 65, 66, 67, 153, 46
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A self-inverse permutation of the natural numbers.
a(1) = 1, a(2) = 3, a(3) = 2, a(p) = p for primes p > 3 and a(u * v) = a(u) * a(v) for u, v > 0.
A permutation of the natural numbers: a(a(n)) = n for all n and a(n) = n iff n = 6^k * m for k >= 0 and m > 0 with gcd(m, 6) = 1 (see A064615).
A000244 and A000079 give record values and where they occur. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 08 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| a(n) = A065330(n) * (2 ^ A007949(n)) * (3 ^ A007814(n)). [Reinhard Zumkeller, Jan 03 2011]
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EXAMPLE
| a(15) = a(3*5) = a(3)*a(5) = 2*5 = 10; a(16) = a(2^4) = a(2)^4 = 3^4 = 81; a(17) = 17; a(18) = a(2*3^2) = a(2)*a(3^2) = 3*a(3)^2 = 3*2^2 = 12.
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PROG
| (Haskell)
a064614 n = f n 1 where
f x y = if m == 0 then f x' (3*y) else g x y where (x', m) = divMod x 2
g x y = if m == 0 then g x' (2*y) else x*y where (x', m) = divMod x 3
-- Reinhard Zumkeller, Jan 03 2011
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CROSSREFS
| A064615.
Sequence in context: A193980 A194001 A178230 * A016650 A033313 A140590
Adjacent sequences: A064611 A064612 A064613 * A064615 A064616 A064617
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KEYWORD
| nonn,mult,nice
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 25 2001
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