A035285 - OEIS

%I #19 Dec 30 2023 16:56:09

%S 1,6,22,32,66,20,192,178,72,120,96,52,704,128,450,432,440,168,576,192,

%T 610,312,2112,768,640,1090,1584,288,1320,296,320,281,1008,360,2112,

%U 1152,392,3660,1144,416,5696,456,2304,244,2816,3840,512,2562,4752,552,1728

%N Similar submodules in cubian ring of index f(n)^2 where f(n) is the n-th positive integer represented by the quadratic form x^2 - 2 y^2.

%H M. Baake and R. V. Moody, <a href="https://doi.org/10.4153/CJM-1999-057-0">Similarity submodules and root systems in four dimensions</a>, Canad. J. Math. (1999), 51 1258-1276.

%H Research Group Michael Baake, <a href="http://www.mathematik.uni-bielefeld.de/baake/preprints.html">Preprints</a>

%o (PARI) g(p, e) = (e+1)*p^e + 2*(1-(e+1)*p^e+e*p^(e+1))/(p-1)^2;

%o fpa(p, e) = {if (p == 2, g(2, e), if (((p % 8) == 3) || ((p % 8) == 5), if (e % 2, 0, g(p^2, e/2)), if (((p % 8) == 1) || ((p % 8) == 7), sum(s=0, e, g(p, s)*g(p, e-s)))));}

%o za(n) = {my(f = factor(n)); prod(i=1, #f~, fpa(f[i, 1], f[i, 2]));}

%o lista(nn) = {for (n=1, nn, if (v = za(n), print1(v, ", ")););} \\ _Michel Marcus_, Mar 03 2014

%Y Cf. A035284.

%K easy,nonn

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Michel Marcus_, Mar 03 2014