A130614 a(n) = p^(p-2), where p = prime(n).

1, 3, 125, 16807, 2357947691, 1792160394037, 2862423051509815793, 5480386857784802185939, 39471584120695485887249589623, 3053134545970524535745336759489912159909

Offset: 1

Author

Jonathan Vos Post, Jun 18 2007

Keywords

• easy
• nonn

Comments

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

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..77

Crossrefs

Cf. A000040, A000272, A004124, A036878.

Programs

Magma

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

Magma

[p^(p-2): p in PrimesUpTo(50)]; // Vincenzo Librandi, Mar 27 2014

Mathematica

Table[Prime@n^(Prime@n - 2), {n, 20}] (* Vincenzo Librandi, Mar 27 2014 *)
#^(#-2)&/@Prime[Range[10]] (* Harvey P. Dale, Oct 18 2016 *)

PARI

a(n) = my(p=prime(n)); p^(p-2) \\ Felix Fröhlich, May 10 2021

Formula

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

For n >= 2, (-1)^((p-1)/2) * a(n) = A004124(p), where p = prime(n). - Jianing Song, May 10 2021

Extensions

Name edited by Felix Fröhlich, May 10 2021