A263830 The number c_{Z^3,pi_1(B_2)}(2n) of 3-torus 2n-coverings over the second amphicosm.

1, 5, 9, 23, 19, 53, 33, 93, 74, 119, 73, 255, 99, 213, 219, 363, 163, 482, 201, 581, 393, 485, 289, 1085, 422, 663, 634, 1047, 451, 1463, 513, 1417, 897, 1103, 915, 2374, 723, 1365, 1227, 2511, 883, 2661, 969, 2399, 2078, 1973, 1153, 4419

Offset

1,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..20000

G. Chelnokov, M. Deryagina, A. Mednykh, On the Coverings of Amphicosms; Revised title: On the coverings of Euclidian manifolds B_1 and B_2, arXiv preprint arXiv:1502.01528 [math.AT], 2015.

Mathematica

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]}];
Array[a, 48] (* Jean-François Alcover, Sep 16 2018, after Gheorghe Coserea *)

Prog

(PARI)
a(n) = {
  1/2 * sumdiv(n, d, sumdiv(n\d, m,
  (sqr(d) + 3/2 + 1/2*(-1)^(d%2) + (-1)^((n\(d*m))%2) +
  (-1)^((d + n\(d*m))%2)) * m));
};
vector(48, n, a(n))  \\ Gheorghe Coserea, May 05 2016

Crossrefs

Cf. A263825-A263830, A263832.

Sequence in context: A219521 A215178 A058893 * A343803 A194802 A229925

Adjacent sequences: A263827 A263828 A263829 * A263831 A263832 A263833

Keyword

nonn

Author

N. J. A. Sloane, Oct 28 2015

Extensions

More terms from Gheorghe Coserea, May 05 2016

Status

approved