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A033845
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Numbers n of the form 2^i*3^j, i and j >= 1.
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63
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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
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OFFSET
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1,1
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COMMENTS
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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
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
So these numbers are called Psi-perfect numbers [see J-M. de Koninck & A. Mercier, problème 654]. - Bernard Schott, Nov 20 2020
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REFERENCES
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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.
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LINKS
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FORMULA
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MATHEMATICA
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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 *)
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PROG
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(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
(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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