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%I #22 May 13 2022 14:05:29
%S 1,5,6,10,24,21,40,30,31,60,64,50,84,120,60,50,144,120,124,85,144,200,
%T 160,126,91,180,240,240,155,204,220,300,410,320,156,264,280,210,360,
%U 300,304,384,420,170,400,504,360,300,364,384,250,400,504,960,424,720,310
%N Expansion of zeta function of icosian ring (nonzero terms).
%C 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).
%C Nonzero terms of A078473. - _Michel Marcus_, Mar 03 2014
%H Amiram Eldar, <a href="/A035282/b035282.txt">Table of n, a(n) for n = 1..10000</a>
%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.
%H M. Baake and R. V. Moody, <a href="http://arXiv.org/abs/math/9904028">Similarity submodules and root systems in four dimensions</a>, arXiv:math/9904028 [math.MG], 1999.
%t 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 *)
%Y Cf. A031363, A035187, A078472, A078473.
%K easy,nonn
%O 1,2
%A _N. J. A. Sloane_.
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