A098096 -id:A098096 - cp's OEIS frontend

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

Reinhard Zumkeller, May 26 2003

nonn

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)).

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

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

Cf. A053810, A006881, A051674.
Cf. A098096, numbers of the form 2^p * p^2.
Cf. A001221, A001222, A001414, A020639, A006530, A051903, A051904.
Cf. A151800.

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

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 *)

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

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

A098880 a(n) = 11^n * n^11.

Original entry on oeis.org

0, 11, 247808, 235782657, 61408804864, 7863818359375, 642717115324416, 38532504363714053, 1841328767004311552, 73994897046174912819, 2593742460100000000000, 81402749386839761113321, 2331878554708454877954048, 61870237399093306018139447, 1537821699264393105232001024

Offset: 0

Parthasarathy Nambi, Oct 14 2004

			11^2 * 2^11 = 247808

Cf. A098096, A097205, A097206.

[ 11^n*n^11: n in [0..20] ]; // Vincenzo Librandi, Feb 04 2011

G.f.: 11*x*(25937424601*x^10 +4800781498876*x^9 +32719096519197*x^8 +42939747452448*x^7 +17251662975954*x^6 +2532405864648*x^5 +142575727074*x^4 +2932842528*x^3 +18469077*x^2 +22396*x +1) / (11*x -1)^12. - Colin Barker, May 01 2013

cp's OEIS Frontend

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

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