A263828 The number c_{P c pi_1(B_1)}(n) of the first amphicosm n-coverings over the first amphicosm.

1, 4, 5, 10, 7, 20, 9, 22, 18, 28, 13, 50, 15, 36, 35, 46, 19, 72, 21, 70, 45, 52, 25, 110, 38, 60, 58, 90, 31, 140, 33, 94, 65, 76, 63, 180, 39, 84, 75, 154, 43, 180, 45, 130, 126, 100, 49, 230, 66, 152, 95, 150, 55, 232, 91, 198, 105, 124, 61

Offset: 1

Author

N. J. A. Sloane, Oct 28 2015

Keywords

• nonn

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.

Crossrefs

Cf. A263825-A263830, A263832.

Programs

Mathematica

a[n_] := Sum[(3/2 + 1/2 (-1)^Mod[d, 2]) DivisorSigma[1, n/d], {d, Divisors[ n]}] - If[OddQ[n], 0, Sum[(3/2 + 1/2 (-1)^Mod[d, 2]) DivisorSigma[1, n/(2 d)], {d, Divisors[n/2]}]];
Array[a, 59] (* Jean-François Alcover, Oct 10 2018, after Gheorghe Coserea *)

PARI

a(n) = {
  sumdiv(n, d, (3/2 + 1/2*(-1)^(d%2)) * sigma(n/d)) -
  if (n%2, 0, sumdiv(n\2, d, (3/2 + 1/2*(-1)^(d%2))*sigma(n\(2*d))))
};
vector(59, n, a(n))  \\ Gheorghe Coserea, May 04 2016

Extensions

More terms from Gheorghe Coserea, May 04 2016