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A263827 The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.

%I A263827 #18 Dec 03 2017 11:12:57
%S A263827 2,6,10,14,14,30,18,30,36,42,26,70,30,54,70,62,38,108,42,98,90,78,50,
%T A263827 150,76,90,116,126,62,210,66,126,130,114,126,252,78,126,150,210,86,
%U A263827 270,90,182,252,150,98,310,132,228,190,210,110,348,182,270,210,186,122,490,126,198,324,254,210,390,138,266,250,378
%N A263827 The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.
%H A263827 Gheorghe Coserea, <a href="/A263827/b263827.txt">Table of n, a(n) for n = 1..20000</a>
%H A263827 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.
%p A263827 A263827 := proc(n)
%p A263827     local locn,a,twol,fourl ;
%p A263827     locn := 2*n ;
%p A263827     # Theorem 3 (iii)
%p A263827     a := 0 ;
%p A263827     for twol in numtheory[divisors](locn) do
%p A263827         if type(twol,'even') then
%p A263827             a := a+numtheory[sigma](locn/twol) ;
%p A263827         end if;
%p A263827     end do:
%p A263827     for fourl in numtheory[divisors](locn) do
%p A263827         if modp(fourl,4) = 0 then
%p A263827             a := a-numtheory[sigma](locn/fourl) ;
%p A263827         end if;
%p A263827     end do:
%p A263827     %*2 ;
%p A263827 end proc: # _R. J. Mathar_, Nov 03 2015
%t A263827 a[n_] := 2*Sum[If[Mod[d,4] == 2, DivisorSigma[1, 2*n/d], 0], {d, Divisors[ 2*n ] } ];
%t A263827 Array[a, 70] (* _Jean-François Alcover_, Dec 03 2017 *)
%o A263827 (PARI)
%o A263827 A007429(n) = sumdiv(n, d, sigma(d));
%o A263827 a(n) = 2*A007429(n) - if(n%2, 0, 2*A007429(n\2));
%o A263827 vector(70, n, a(n))  \\ _Gheorghe Coserea_, May 04 2016
%Y A263827 Cf. A263825-A263830, A263832.
%K A263827 nonn
%O A263827 1,1
%A A263827 _N. J. A. Sloane_, Oct 28 2015