A130614 - OEIS

%I #21 Sep 08 2022 08:45:30

%S 1,3,125,16807,2357947691,1792160394037,2862423051509815793,

%T 5480386857784802185939,39471584120695485887249589623,

%U 3053134545970524535745336759489912159909

%N a(n) = p^(p-2), where p = prime(n).

%C Number of labeled trees on p(n) nodes, where p(n) is the n-th prime.

%C Let p = prime(n). For n >= 2, (-1)^((p-1)/2) * a(n) is the discriminant of the p-th cyclotomic polynomial. - _Jianing Song_, May 10 2021

%H Vincenzo Librandi, <a href="/A130614/b130614.txt">Table of n, a(n) for n = 1..77</a>

%F a(n) = A000272(A000040(n)).

%F For n >= 2, (-1)^((p-1)/2) * a(n) = A004124(p), where p = prime(n). - _Jianing Song_, May 10 2021

%t Table[Prime@n^(Prime@n - 2), {n, 20}] (* _Vincenzo Librandi_, Mar 27 2014 *)

%t #^(#-2)&/@Prime[Range[10]] (* _Harvey P. Dale_, Oct 18 2016 *)

%o (Magma) [n^(n-2) : n in [2..40] | IsPrime(n)];

%o (Magma) [p^(p-2): p in PrimesUpTo(50)]; // _Vincenzo Librandi_, Mar 27 2014

%o (PARI) a(n) = my(p=prime(n)); p^(p-2) \\ _Felix Fröhlich_, May 10 2021

%Y Cf. A000040, A000272, A004124, A036878.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Jun 18 2007

%E Name edited by _Felix Fröhlich_, May 10 2021