A035284 - OEIS

%I #16 Mar 03 2014 11:05:13

%S 1,10,12,20,48,66,80,120,97,120,128,200,168,480,240,100,576,240,248,

%T 370,288,800,320,792,281,360,960,960,970,408,440,1200,1394,1280,672,

%U 528,560,1320,1440,600,608,1536,1680,340,1600,3168,720,2400,728,768,1000

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

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

%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 == 5, g(5, e), if (((p % 5) == 2) || ((p % 5) == 3), if (e % 2, 0, g(p^2, e/2)), if (((p % 5) == 1) || ((p % 5) == 4), 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. A035285.

%K easy,nonn

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Michel Marcus_, Mar 03 2014