The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A082949 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A082949

Numbers of the form p^q * q^p, with distinct primes p and q.
(history; published version)

#29 by Alonso del Arte at Wed Jul 18 15:05:41 EDT 2018

EXAMPLE

2^3 7 * 37^2 = 8 128* 9 49 = 726272, therefore 6272 is in the sequence.

2^5 * 5^2 = 32 * 25 = 800.

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

678223072849 = 7^7 * 7^7 is not in the sequence

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[{nmax nn= 30}, Take[Union[First[#]^Last[#] Last[#]^First[#] &/@ Subsets[ Prime[Range[nmaxnn]], {2}]], nmaxnn]] (* Harvey P. Dale, Aug 19 2012 *)

KEYWORD

nonn,changed

nonn

STATUS

editing

approved

#28 by Alonso del Arte at Wed Jul 11 00:36:49 EDT 2018

EXAMPLE

678223072849 = 7^7 * 7^7 is not in the sequence

Discussion

Wed Jul 18

05:02

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A082949 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#27 by Alonso del Arte at Wed Jul 04 02:41:53 EDT 2018

MATHEMATICA

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 *)

#26 by Alonso del Arte at Wed Jun 20 02:20:39 EDT 2018

EXAMPLE

2^3 * 3^2 = 8 * 9 = 72.

Discussion

Wed Jun 27

04:11

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A082949 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#25 by Alonso del Arte at Wed Jun 13 07:40:21 EDT 2018

EXAMPLE

2^5 * 5^2 = 32 * 25 = 800.

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

#24 by Alonso del Arte at Wed Jun 06 02:36:23 EDT 2018

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[{nnnmax = 30}, Take[Union[First[#]^Last[#] Last[#]^First[#] &/@ Subsets[ Prime[Range[nnnmax]], {2}]], nn nmax]] (* Harvey P. Dale, Aug 19 2012 *)

STATUS

approved

editing

Discussion

Wed Jun 06

02:36

Alonso del Arte: I'm inclined to delete what I wrote in 2005 here...

#23 by Reinhard Zumkeller at Sat Feb 07 16:48:05 EST 2015

STATUS

editing

approved

#22 by Reinhard Zumkeller at Sat Feb 07 16:47:43 EST 2015

COMMENTS

A001221(a(n)) = 2;

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)).

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

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

CROSSREFS

Cf. A151800A001221, A001222, A001414, A020639, A006530, A051903, A051904.

Cf. A151800.

#21 by Reinhard Zumkeller at Sat Feb 07 16:28:14 EST 2015

PROG

(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

CROSSREFS

Cf. A151800.

#20 by Reinhard Zumkeller at Sat Feb 07 16:26:29 EST 2015

LINKS

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

STATUS

approved

editing