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A130614 a(n) = p^(p-2), where p = prime(n). 2
1, 3, 125, 16807, 2357947691, 1792160394037, 2862423051509815793, 5480386857784802185939, 39471584120695485887249589623, 3053134545970524535745336759489912159909 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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

MATHEMATICA

Table[Prime@n^(Prime@n - 2), {n, 20}] (* Vincenzo Librandi, Mar 27 2014 *)

#^(#-2)&/@Prime[Range[10]] (* Harvey P. Dale, Oct 18 2016 *)

PROG

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

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

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

CROSSREFS

Cf. A000040, A000272, A004124, A036878.

Sequence in context: A219010 A037118 A085531 * A114877 A152859 A241647

Adjacent sequences:  A130611 A130612 A130613 * A130615 A130616 A130617

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jun 18 2007

EXTENSIONS

Name edited by Felix Fröhlich, May 10 2021

STATUS

approved

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Last modified August 5 10:01 EDT 2021. Contains 346464 sequences. (Running on oeis4.)