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A082949
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Numbers of the form p^q * q^p, with distinct primes p and q.
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7
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72, 800, 6272, 30375, 247808, 750141, 1384448, 37879808, 189267968, 235782657, 1313046875, 3502727631, 4437573632, 451508436992, 634465620819, 2063731785728, 7863818359375, 7971951402153, 188153927303168, 453238525390625, 1145440056788109
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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2^7 * 7^2 = 128*49 = 6272, therefore 6272 is in the sequence.
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MATHEMATICA
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Take[Union[Select[Flatten[Table[If[p != q, Prime[p]^Prime[q]*Prime[q]^Prime[p]], {p, 100}, {q, 100}]], IntegerQ]], 30] (* Alonso del Arte, Oct 28 2005 *)
Select[Range[10! ], Length[FactorInteger[ # ]]==2&&FactorInteger[ # ][[1, 1]]==FactorInteger[ # ][[2, 2]]&&FactorInteger[ # ][[1, 2]]==FactorInteger[ # ][[2, 1]]&] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2010 *)
With[{nn=30}, Take[Union[First[#]^Last[#] Last[#]^First[#]&/@ Subsets[ Prime[Range[nn]], {2}]], nn]] (* Harvey P. Dale, Aug 19 2012 *)
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PROG
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(PARI) term(p, q)=p^q*q^p;
l=listcreate(465); for(m=1, 30, for(n=m+1, 31, listput(l, term(prime(m), prime(n))))); listsort(l) \\ Rick L. Shepherd, Sep 07 2003
(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a082949 n = a082949_list !! (n-1)
a082949_list = f $ singleton (2 ^ 3 * 3 ^ 2, 2, 3) where
f s = y : f (if p' < q then insert (p' ^ q * q ^ p', p', q) s'' else s'')
where s'' = insert (p ^ q' * q' ^ p, p, q') s'
p' = a151800 p; q' = a151800 q
((y, p, q), s') = deleteFindMin s
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CROSSREFS
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Cf. A098096, numbers of the form 2^p * p^2.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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