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

1,2

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_] := 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 *)

Prog

(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

Crossrefs

Cf. A263825-A263830, A263832.

Sequence in context: A215754 A226486 A060648 * A327577 A092961 A327614

Adjacent sequences: A263825 A263826 A263827 * A263829 A263830 A263831

Keyword

nonn

Author

N. J. A. Sloane, Oct 28 2015

Extensions

More terms from Gheorghe Coserea, May 04 2016

Status

approved