

A162408


Solutions x to the equation x^xy^y = some prime number for any y.


0



2, 3, 4, 5, 7, 8, 11, 13, 15, 17, 19, 23, 26, 30, 42, 47, 53, 65, 73, 77, 84, 92, 100, 101, 106, 110, 116, 120, 122, 122, 124, 133, 137, 163, 167, 173, 173
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OFFSET

1,1


COMMENTS

These are the numbers a in the definition of A068146.
If there are two solutions, like with (x,y) = (17,12) and (x,y) = (17,16) with
the same x, only one instance of x is placed into the sequence, so there is no
1to1 correspondence with terms in A068146.
The corresponding set of y contains at least the numbers 1 to 6, 10, 12, 14, 16, 17, 19, 20, 22 etc


LINKS

Table of n, a(n) for n=1..37.


EXAMPLE

Triples (x,y,prime) are (2,1,3), (3,2,23), (4,3,229), (5,2,3121), (7,6,776887),
(8,5,16774091), (11,10,275311670611), (13,6,302875106545597), (15,4,437893890380859119),
(17,12,827240252970236315921), (17,16,808793517812627212561) etc


MATHEMATICA

f[a_, b_]:=a^ab^b; lst={}; Do[Do[If[a>b, p=f[a, b]]; If[PrimeQ[p], AppendTo[lst, a]], {b, 4*4!}], {a, 5*4!}]; Union[lst]


CROSSREFS

Cf. A068146
Sequence in context: A269870 A307824 A081730 * A348284 A162721 A176176
Adjacent sequences: A162405 A162406 A162407 * A162409 A162410 A162411


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Jul 02 2009


EXTENSIONS

Edited and extended by R. J. Mathar, Sep 16 2009


STATUS

approved



