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 A271936 Commutative powers: numbers of the form a^b = b^a. 0
 1, 4, 16, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 10000000000, 285311670611, 8916100448256, 302875106592253, 11112006825558016, 437893890380859375, 18446744073709551616, 827240261886336764177, 39346408075296537575424, 1978419655660313589123979, 104857600000000000000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The only integer solutions (a,b) to the equation a^b = b^a are (k,k) for k >= 1, (2,4), and (4,2). Suppose ae. 2 will because 2^4 = 4^2 and since we have a bijection this is the only solution. LINKS FORMULA a(n+1) = A000302(n), n=0, n=1, n=2; a(n+1) = A000312(n), n>2. EXAMPLE 4 is in the list because 2^2 = 2^2; 16 is in the list because 2^4 = 4^2. MATHEMATICA Union[Power @@@ Select[Tuples[Range@ 20, 2], Power @@ # == Power @@ Reverse@ # &]] (* Michael De Vlieger, Apr 17 2016 *) CROSSREFS Sequence in context: A067688 A097374 A257309 * A046358 A046366 A227609 Adjacent sequences:  A271933 A271934 A271935 * A271937 A271938 A271939 KEYWORD nonn,easy AUTHOR Natan Arie' Consigli, Apr 16 2016 STATUS approved

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Last modified July 22 15:00 EDT 2019. Contains 325224 sequences. (Running on oeis4.)