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 A082949 Numbers of the form p^q * q^p, with distinct primes p and q. 4

%I

%S 72,800,6272,30375,247808,750141,1384448,37879808,189267968,235782657,

%T 1313046875,3502727631,4437573632,451508436992,634465620819,

%U 2063731785728,7863818359375,7971951402153,188153927303168,453238525390625,1145440056788109

%N Numbers of the form p^q * q^p, with distinct primes p and q.

%C A001221(a(n)) = 2;

%C A001222(a(n)) = A001414(a(n)) = A020639(a(n)) + A006530(a(n)) = A051904(a(n)) + A051903(a(n));

%C A020639(a(n)) = A051904(a(n));

%C A006530(a(n)) = A051903(a(n)).

%H Reinhard Zumkeller, <a href="/A082949/b082949.txt">Table of n, a(n) for n = 1..1000</a>

%e 2^7 * 7^2 = 128*49 = 6272, therefore 6272 is in the sequence.

%t 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 *)

%t 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 *)

%t With[{nn=30},Take[Union[First[#]^Last[#] Last[#]^First[#]&/@ Subsets[ Prime[Range[nn]],{2}]],nn]] (* _Harvey P. Dale_, Aug 19 2012 *)

%o (PARI) term(p,q)=p^q*q^p;

%o 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

%o import Data.Set (singleton, deleteFindMin, insert)

%o a082949 n = a082949_list !! (n-1)

%o a082949_list = f \$ singleton (2 ^ 3 * 3 ^ 2, 2, 3) where

%o f s = y : f (if p' < q then insert (p' ^ q * q ^ p', p', q) s'' else s'')

%o where s'' = insert (p ^ q' * q' ^ p, p, q') s'

%o p' = a151800 p; q' = a151800 q

%o ((y, p, q), s') = deleteFindMin s

%o -- _Reinhard Zumkeller_, Feb 07 2015

%Y Cf. A053810, A006881, A051674.

%Y Cf. A098096, numbers of the form 2^p * p^2.

%Y Cf. A001221, A001222, A001414, A020639, A006530, A051903, A051904.

%Y Cf. A151800.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, May 26 2003

%E Corrected and extended by _Rick L. Shepherd_, Sep 07 2003

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)