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A003474
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Generalized Euler phi function (for p=3).
(Formerly M3541)
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4
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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; internal format)
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OFFSET
| 1,2
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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
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REFERENCES
| J. T. B. Beard, Jr. and K. I. West, Factorization tables for x^n-1 over GF(q), Math. Comp., 28 (1974), 1167-1168.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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PROG
| (PARI)
p=3; /* global */
num_normal_p(n)=
{
local( 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)=
{
local( 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)) /* show terms */ /* Joerg Arndt, Jul 03 2011 */
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CROSSREFS
| Cf. A003473 (p=2), A192037(p=5).
Sequence in context: A049726 A130656 A053191 * A095823 A092116 A083969
Adjacent sequences: A003471 A003472 A003473 * A003475 A003476 A003477
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KEYWORD
| nonn,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Terms > 86093440 by Joerg Arndt, Jul 03 2011.
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