cp's OEIS Frontend

A263829 Total number c_{pi_1(B_2)}(n) of n-coverings over the second amphicosm.

%I A263829 #16 May 05 2016 02:40:18
%S A263829 1,3,5,13,7,19,9,43,18,33,13,93,15,51,35,137,19,110,21,175,45,99,25,
%T A263829 355,38,129,58,285,31,289,33,455,65,201,63,626,39,243,75,721,43,483,
%U A263829 45,589,126,339,49,1305,66,498,95,783,55,750,91,1227
%N A263829 Total number c_{pi_1(B_2)}(n) of n-coverings over the second amphicosm.
%H A263829 Gheorghe Coserea, <a href="/A263829/b263829.txt">Table of n, a(n) for n = 1..20000</a>
%H A263829 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.
%o A263829 (PARI)
%o A263829 A001001(n) = sumdiv(n, d, sigma(d) * d);
%o A263829 A007429(n) = sumdiv(n, d, sigma(d));
%o A263829 A007434(n) = sumdiv(n, d, moebius(n\d) * d^2);
%o A263829 A059376(n) = sumdiv(n, d, moebius(n\d) * d^3);
%o A263829 A060640(n) = sumdiv(n, d, sigma(n\d) * d);
%o A263829 EpiPcZn(n) = sumdiv(n, d, moebius(n\d) * d^2 * gcd(d,2));
%o A263829 S1(n)      = if (n%2, 0, A001001(n\2));
%o A263829 S11(n)     = A060640(n) - if(n%2, 0, A060640(n\2));
%o A263829 S21(n)     = if (n%2, 0, 2*A060640(n\2)) - if (n%4, 0, 2*A060640(n\4));
%o A263829 S22(n)     = { if (n%2, A060640(n), if (n%4, 0,
%o A263829   sumdiv(n\4, d, 2*d*(sigma(n\(2*d)) - sigma(n\(4*d))))));
%o A263829 };
%o A263829 A027844(n) = S1(n) + S11(n) + S21(n);
%o A263829 a(n) = { 1/n * sumdiv(n, d,
%o A263829   A059376(d) * S1(n\d) + EpiPcZn(d) * S21(n\d) + A007434(d) * S22(n\d));
%o A263829 };
%o A263829 vector(56, n, a(n))  \\ _Gheorghe Coserea_, May 04 2016
%Y A263829 Cf. A263825-A263830, A263832.
%K A263829 nonn
%O A263829 1,2
%A A263829 _N. J. A. Sloane_, Oct 28 2015
%E A263829 More terms from _Gheorghe Coserea_, May 04 2016