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The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.
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%I #18 Dec 03 2017 11:12:57

%S 2,6,10,14,14,30,18,30,36,42,26,70,30,54,70,62,38,108,42,98,90,78,50,

%T 150,76,90,116,126,62,210,66,126,130,114,126,252,78,126,150,210,86,

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

%H Gheorghe Coserea, <a href="/A263827/b263827.txt">Table of n, a(n) for n = 1..20000</a>

%H 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 := proc(n)

%p local locn,a,twol,fourl ;

%p locn := 2*n ;

%p # Theorem 3 (iii)

%p a := 0 ;

%p for twol in numtheory[divisors](locn) do

%p if type(twol,'even') then

%p a := a+numtheory[sigma](locn/twol) ;

%p end if;

%p end do:

%p for fourl in numtheory[divisors](locn) do

%p if modp(fourl,4) = 0 then

%p a := a-numtheory[sigma](locn/fourl) ;

%p end if;

%p end do:

%p %*2 ;

%p end proc: # _R. J. Mathar_, Nov 03 2015

%t a[n_] := 2*Sum[If[Mod[d,4] == 2, DivisorSigma[1, 2*n/d], 0], {d, Divisors[ 2*n ] } ];

%t Array[a, 70] (* _Jean-François Alcover_, Dec 03 2017 *)

%o (PARI)

%o A007429(n) = sumdiv(n, d, sigma(d));

%o a(n) = 2*A007429(n) - if(n%2, 0, 2*A007429(n\2));

%o vector(70, n, a(n)) \\ _Gheorghe Coserea_, May 04 2016

%Y Cf. A263825-A263830, A263832.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Oct 28 2015