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A003473
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Generalized Euler phi function (for p=2).
(Formerly M0875)
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6
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1, 2, 3, 8, 15, 24, 49, 128, 189, 480, 1023, 1536, 4095, 6272, 10125, 32768, 65025, 96768, 262143, 491520, 583443, 2095104, 4190209, 6291456, 15728625, 33546240, 49545027, 102760448, 268435455, 331776000, 887503681, 2147483648, 3211797501, 8522956800, 12325233375, 25367150592, 68719476735, 137438429184, 206007472125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is the number of n X n circulant invertible matrices over GF(2) . - Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 20 2003
a(n) = n*A027362(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 09 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=2; /* 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)=n * num_normal(n);
v=vector(66, n, a(n)) /* show terms */ /* Joerg Arndt, Jul 03 2011 */
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CROSSREFS
| Cf. A003474 (p=3), A192037 (p=5).
Cf. A086479.
Sequence in context: A122412 A174019 A128035 * A095373 A056802 A179991
Adjacent sequences: A003470 A003471 A003472 * A003474 A003475 A003476
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 09 2003
Terms >331776000 by Joerg Arndt, Jul 03 2011.
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