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%I #16 Sep 16 2018 17:17:26
%S 1,5,9,23,19,53,33,93,74,119,73,255,99,213,219,363,163,482,201,581,
%T 393,485,289,1085,422,663,634,1047,451,1463,513,1417,897,1103,915,
%U 2374,723,1365,1227,2511,883,2661,969,2399,2078,1973,1153,4419
%N The number c_{Z^3,pi_1(B_2)}(2n) of 3-torus 2n-coverings over the second amphicosm.
%H Gheorghe Coserea, <a href="/A263830/b263830.txt">Table of n, a(n) for n = 1..20000</a>
%H G. Chelnokov, M. Deryagina, A. Mednykh, <a href="http://arxiv.org/abs/1502.01528">On the Coverings of Amphicosms; Revised title: On the coverings of Euclidian manifolds B_1 and B_2</a>, arXiv preprint arXiv:1502.01528 [math.AT], 2015.
%t a[n_] := 1/2 Sum[Sum[(d^2 + 3/2 + 1/2 (-1)^Mod[d, 2] + (-1)^Mod[Quotient[n, d m], 2] + (-1)^Mod[d+Quotient[n, d m], 2])m, {m, Divisors[Quotient[n, d] ]}], {d, Divisors[n]}];
%t Array[a, 48] (* _Jean-François Alcover_, Sep 16 2018, after _Gheorghe Coserea_ *)
%o (PARI)
%o a(n) = {
%o 1/2 * sumdiv(n, d, sumdiv(n\d, m,
%o (sqr(d) + 3/2 + 1/2*(-1)^(d%2) + (-1)^((n\(d*m))%2) +
%o (-1)^((d + n\(d*m))%2)) * m));
%o };
%o vector(48, n, a(n)) \\ _Gheorghe Coserea_, May 05 2016
%Y Cf. A263825-A263830, A263832.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 28 2015
%E More terms from _Gheorghe Coserea_, May 05 2016
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