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A003474 Generalized Euler phi function (for p=3).
(Formerly M3541)
4
1, 4, 18, 32, 160, 324, 1456, 2048, 13122, 25600, 117128, 209952, 913952, 2119936, 9447840, 13107200, 86093440, 172186884, 774840976, 1310720000, 6964002864, 13718968384, 62761410632, 88159684608, 557885504000, 835308258304, 5083731656658, 8988257288192, 45753584909920, 89261680665600, 411782264189296, 564050001920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>=2 a(n) is the number of n X n circulant invertible matrices over GF(3). - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 22 2003

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..32.

J. T. B. Beard Jr. and K. I. West, Factorization tables for x^n-1 over GF(q), Math. Comp., 28 (1974), 1167-1168.

MATHEMATICA

p = 3; numNormalp[n_] := Module[{r, i, pp}, pp = 1; Do[r = MultiplicativeOrder[p, d]; i = EulerPhi[d]/r; pp *= (1-1/p^r)^i, {d, Divisors[n]}]; Return[pp]]; numNormal[n_] := Module[{t, q, pp}, t=1; q=n; While[0==Mod[q, p], q /= p; t += 1]; pp = numNormalp[q]; pp *= p^n/n; Return[pp]]; a[n_] := If[n==1, 1, n*numNormal[n]]; Array[a, 40] (* Jean-Fran├žois Alcover, Dec 10 2015, after Joerg Arndt *)

PROG

(PARI)

p=3; /* global */

num_normal_p(n)=

{

    my( r, i, pp );

    pp = 1;

    fordiv (n, d,

        r = znorder(Mod(p, d));

        i = eulerphi(d)/r;

        pp *= (1 - 1/p^r)^i;

    );

    return( pp );

}

num_normal(n)=

{

    my( t, q, pp );

    t = 1;  q = n;

    while ( 0==(q%p), q/=p; t+=1; );

    /* here: n==q*p^t */

    pp = num_normal_p(q);

    pp *= p^n/n;

    return( pp );

}

a(n)=if ( n==1, 1, n * num_normal(n) );

v=vector(66, n, a(n))

/* Joerg Arndt, Jul 03 2011 */

CROSSREFS

Cf. A003473 (p=2), A192037 (p=5).

Sequence in context: A130656 A292161 A053191 * A095823 A092116 A083969

Adjacent sequences:  A003471 A003472 A003473 * A003475 A003476 A003477

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Terms > 86093440 from Joerg Arndt, Jul 03 2011

STATUS

approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)