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 A064614 Exchange 2 and 3 in the prime factorization of n. 13
 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; text; internal format)
 OFFSET 1,2 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. - Reinhard Zumkeller, Feb 08 2010 Completely multiplicative with a(2) = 3, a(3) = 2, and a(p) = p for primes p > 3. - Charles R Greathouse IV, Jun 28 2015 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 A. B. Frizell, Certain non-enumerable sets of infinite permutations. Bull. Amer. Math. Soc. 21 (1915), no. 10, 495-499. FORMULA a(n) = A065330(n) * (2 ^ A007949(n)) * (3 ^ A007814(n)). - Reinhard Zumkeller, Jan 03 2011 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. MATHEMATICA a[n_] := Times @@ Power @@@ (FactorInteger[n] /. {2, e2_} -> {0, e2} /. {3, e3_} -> {2, e3} /. {0, e2_} -> {3, e2}); Table[a[n], {n, 1, 69}] (* Jean-François Alcover, Nov 20 2012 *) a[n_] := n * Times @@ ({3/2, 2/3}^IntegerExponent[n, {2, 3}]); Array[a, 100] (* Amiram Eldar, Sep 20 2020 *) PROG (Haskell) a064614 1 = 1 a064614 n = product \$ map f \$ a027746_row n where    f 2 = 3; f 3 = 2; f p = p -- Reinhard Zumkeller, Apr 09 2012, Jan 03 2011 (Python) from operator import mul from functools import reduce from sympy import factorint def A064614(n):     return reduce(mul, ((5-p if 2<=p<=3 else p)**e for p, e in factorint(n).items())) if n > 1 else n # Chai Wah Wu, Dec 27 2014 (PARI) a(n)=my(x=valuation(n, 2)-valuation(n, 3)); n*2^-x*3^x \\ Charles R Greathouse IV, Jun 28 2015 CROSSREFS Cf. A064615, A000244, A000079, A253046, A253047, A027746. Sequence in context: A268824 A306470 A251560 * A234747 A016650 A033313 Adjacent sequences:  A064611 A064612 A064613 * A064615 A064616 A064617 KEYWORD nonn,mult,nice,easy AUTHOR Reinhard Zumkeller, Sep 25 2001 STATUS approved

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Last modified September 28 02:47 EDT 2022. Contains 357063 sequences. (Running on oeis4.)