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%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
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