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

%I A263828 #16 Oct 10 2018 03:26:47
%S A263828 1,4,5,10,7,20,9,22,18,28,13,50,15,36,35,46,19,72,21,70,45,52,25,110,
%T A263828 38,60,58,90,31,140,33,94,65,76,63,180,39,84,75,154,43,180,45,130,126,
%U A263828 100,49,230,66,152,95,150,55,232,91,198,105,124,61
%N A263828 The number c_{P c pi_1(B_1)}(n) of the first amphicosm n-coverings over the first amphicosm.
%H A263828 Gheorghe Coserea, <a href="/A263828/b263828.txt">Table of n, a(n) for n = 1..20000</a>
%H A263828 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 A263828 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]}]];
%t A263828 Array[a, 59] (* _Jean-François Alcover_, Oct 10 2018, after _Gheorghe Coserea_ *)
%o A263828 (PARI)
%o A263828 a(n) = {
%o A263828   sumdiv(n, d, (3/2 + 1/2*(-1)^(d%2)) * sigma(n/d)) -
%o A263828   if (n%2, 0, sumdiv(n\2, d, (3/2 + 1/2*(-1)^(d%2))*sigma(n\(2*d))))
%o A263828 };
%o A263828 vector(59, n, a(n))  \\ _Gheorghe Coserea_, May 04 2016
%Y A263828 Cf. A263825-A263830, A263832.
%K A263828 nonn
%O A263828 1,2
%A A263828 _N. J. A. Sloane_, Oct 28 2015
%E A263828 More terms from _Gheorghe Coserea_, May 04 2016