A035282 Expansion of zeta function of icosian ring (nonzero terms).

1, 5, 6, 10, 24, 21, 40, 30, 31, 60, 64, 50, 84, 120, 60, 50, 144, 120, 124, 85, 144, 200, 160, 126, 91, 180, 240, 240, 155, 204, 220, 300, 410, 320, 156, 264, 280, 210, 360, 300, 304, 384, 420, 170, 400, 504, 360, 300, 364, 384, 250, 400, 504, 960, 424, 720, 310

Offset

1,2

Comments

Let zetaI(s) be the zeta function of icosian ring: zetaI(s) = zetaQ(tau)(2s)*zetaQ(tau)(2s-1) where zetaQ(tau)(s) is defined in A035187; then zetaI(s) = Sum_{n>=1} a(n)/n^(2s).

Nonzero terms of A078473. - Michel Marcus, Mar 03 2014

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

M. Baake and R. V. Moody, Similarity submodules and root systems in four dimensions, arXiv:math/9904028 [math.MG], 1999.

Mathematica

f[p_, e_] := Which[p == 5, (5^(e + 1) - 1)/4, (m = Mod[p, 5]) == 2 || m == 3, If[EvenQ[e], (p^(e + 2) - 1)/(p^2 - 1), 0], m == 1 || m == 4, Sum[(k + 1)*(e - k + 1)*p^k, {k, 0, e}]]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 0 &] (* Amiram Eldar, May 13 2022 *)

Crossrefs

Cf. A031363, A035187, A078472, A078473.

Sequence in context: A056050 A274554 A035111 * A075156 A075904 A018834

Adjacent sequences: A035279 A035280 A035281 * A035283 A035284 A035285

Keyword

easy,nonn

Author

N. J. A. Sloane.

Status

approved