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 A033845 Numbers n of the form 2^i*3^j, i and j >= 1. 53
 6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 162, 192, 216, 288, 324, 384, 432, 486, 576, 648, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2304, 2592, 2916, 3072, 3456, 3888, 4374, 4608, 5184, 5832, 6144, 6912, 7776, 8748, 9216, 10368, 11664 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Solutions to phi(n)=n/3 [See J-M. de Koninck & A. Mercier, problème 733]. Numbers n such that Sum_{d prime divisor of n} 1/d = 5/6. - Benoit Cloitre, Apr 13 2002 Also n such that Sum_{d|n} mu(d)^2/d = 2. - Benoit Cloitre, Apr 15 2002 Complement of A006899 with respect to A003586. - Reinhard Zumkeller, Sep 25 2008 In the sieve of Eratosthenes, if one crosses numbers off multiple times, these numbers are crossed off twice, first for 2 and then for 3. - Alonso del Arte, Aug 22 2011 Subsequence of A051037. - Reinhard Zumkeller, Sep 13 2011 Numbers n such that Sum_{d|n} A008683(d)*A000041(d) = 7. - Carl Najafi, Oct 19 2011 Numbers n such that Sum_{d|n} A008683(d)*A000700(d) = 2. - Carl Najafi, Oct 20 2011 Solutions to the equation A001615(x) = 2x. - Enrique Pérez Herrero, Jan 02 2012 So these numbers are called Psi-perfect numbers [see J-M. de Koninck & A. Mercier, problème 654]. - Bernard Schott, Nov 20 2020 REFERENCES J-M. de Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Ellipses, 2004, Problème 733, page 94. J-M. de Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Ellipses, 2004, Problème 654, page 85. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA Six times the 3-smooth numbers (A003586). - Ralf Stephan, Apr 16 2004 A086411(a(n)) - A086410(a(n)) = 1. - Reinhard Zumkeller, Sep 25 2008 A143201(a(n)) = 2. - Reinhard Zumkeller, Sep 13 2011 a(n) = 2^A191475(n) * 3^A191476(n). - Zak Seidov, Nov 01 2013 Sum_{n>=1} 1/a(n) = 1/2. - Amiram Eldar, Oct 13 2020 MATHEMATICA mx = 12000; Sort@ Flatten@ Table[2^i*3^j, {i, Log[2, mx]}, {j, Log[3, mx/2^i]}] (* Robert G. Wilson v, Aug 17 2012 *) PROG (Haskell) import Data.Set (singleton, deleteFindMin, insert) a033845 n = a033845_list !! (n-1) a033845_list = f (singleton (2*3)) where    f s = m : f (insert (2*m) \$ insert (3*m) s') where      (m, s') = deleteFindMin s -- Reinhard Zumkeller, Sep 13 2011 (PARI) list(lim)=my(v=List(), N); for(n=0, log(lim\2)\log(3), N=6*3^n; while(N<=lim, listput(v, N); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jan 02 2012 CROSSREFS Subsequence of A000423, A003586, A051037, A256617. Cf. A001615, A006899, A086410, A086411, A008683, A143201. Cf. A191475, A191476. Sequence in context: A244193 A329878 A215142 * A187778 A120942 A147306 Adjacent sequences:  A033842 A033843 A033844 * A033846 A033847 A033848 KEYWORD nonn,easy,changed AUTHOR EXTENSIONS Minor edits by N. J. A. Sloane, Jan 31 2010 STATUS approved

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Last modified December 2 01:48 EST 2020. Contains 338864 sequences. (Running on oeis4.)