A035285 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.

1, 6, 22, 32, 66, 20, 192, 178, 72, 120, 96, 52, 704, 128, 450, 432, 440, 168, 576, 192, 610, 312, 2112, 768, 640, 1090, 1584, 288, 1320, 296, 320, 281, 1008, 360, 2112, 1152, 392, 3660, 1144, 416, 5696, 456, 2304, 244, 2816, 3840, 512, 2562, 4752, 552, 1728

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.

Research Group Michael Baake, Preprints

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 == 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))))); }
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. A035284.

Sequence in context: A276795 A037204 A296981 * A069824 A015709 A020195

Adjacent sequences: A035282 A035283 A035284 * A035286 A035287 A035288

Keyword

easy,nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Mar 03 2014

Status

approved