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A064614 Exchange 2 and 3 in the prime factorization of n. 11
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.

Index to divisibility sequences

Index entries for sequences that are permutations of the natural numbers

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-Fran├žois Alcover, Nov 20 2012 *)

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: A178230 A268824 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 March 29 21:48 EDT 2017. Contains 284288 sequences.