A035284 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.

1, 10, 12, 20, 48, 66, 80, 120, 97, 120, 128, 200, 168, 480, 240, 100, 576, 240, 248, 370, 288, 800, 320, 792, 281, 360, 960, 960, 970, 408, 440, 1200, 1394, 1280, 672, 528, 560, 1320, 1440, 600, 608, 1536, 1680, 340, 1600, 3168, 720, 2400, 728, 768, 1000

Offset

1,2

Links

Table of n, a(n) for n=1..51.

M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, Canad. J. Math. (1999), 51 1258-1276.

Prog

(PARI) g(p, e) = (e+1)*p^e + 2*(1-(e+1)*p^e+e*p^(e+1))/(p-1)^2;
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))))); }
za(n) = {my(f = factor(n)); prod(i=1, #f~, fpa(f[i, 1], f[i, 2])); }
lista(nn) = {for (n=1, nn, if (v = za(n), print1(v, ", ")); ); } \\ Michel Marcus, Mar 03 2014

Crossrefs

Cf. A035285.

Sequence in context: A162189 A186438 A346678 * A265403 A215940 A368550

Adjacent sequences: A035281 A035282 A035283 * A035285 A035286 A035287

Keyword

easy,nonn

Author

N. J. A. Sloane.

Extensions

More terms from Michel Marcus, Mar 03 2014

Status

approved