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

72, 800, 6272, 30375, 247808, 750141, 1384448, 37879808, 189267968, 235782657, 1313046875, 3502727631, 4437573632, 451508436992, 634465620819, 2063731785728, 7863818359375, 7971951402153, 188153927303168, 453238525390625, 1145440056788109

Offset: 1

Author

Reinhard Zumkeller, May 26 2003

Keywords

• nonn

Comments

A001221(a(n)) = 2;

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

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

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A053810, A006881, A051674.

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

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

Cf. A151800.

Programs

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
-- Reinhard Zumkeller, Feb 07 2015

Mathematica

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 *)

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

Extensions

Corrected and extended by Rick L. Shepherd, Sep 07 2003