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 A003473 Generalized Euler phi function (for p=2). (Formerly M0875) 10
 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; text; internal format)
 OFFSET 1,2 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 J. T. B. Beard Jr. and K. I. West, Factorization tables for x^n-1 over GF(q), Math. Comp., 28 (1974), 1167-1168. Swee Hong Chan, Henk D. L. Hollmann, Dmitrii V. Pasechnik, Sandpile groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields, arXiv:1405.0113 [math.CO], (1-May-2014) FORMULA a(n) = n * A027362(n). - Vladeta Jovovic, Sep 09 2003 MATHEMATICA p = 2; 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_] := n*numNormal[n]; Array[a, 40] (* Jean-François Alcover, Dec 10 2015, after Joerg Arndt *) PROG (PARI) p=2; /* 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)=n * num_normal(n); v=vector(66, n, a(n)) /* Joerg Arndt, Jul 03 2011 */ CROSSREFS Cf. A003474 (p=3), A192037 (p=5). Cf. also A086479, A027362. Sequence in context: A356371 A293389 A128035 * A095373 A249357 A291400 Adjacent sequences: A003470 A003471 A003472 * A003474 A003475 A003476 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from Vladeta Jovovic, Sep 09 2003 Terms > 331776000 from Joerg Arndt, Jul 03 2011 STATUS approved

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Last modified May 23 21:14 EDT 2024. Contains 372765 sequences. (Running on oeis4.)