A027844 -id:A027844 - cp's OEIS frontend

A046524 Number of coverings of Klein bottle with n lists.

1, 3, 2, 5, 2, 7, 2, 8, 3, 8, 2, 13, 2, 9, 4, 13, 2, 14, 2, 16, 4, 11, 2, 23, 3, 12, 4, 19, 2, 22, 2, 22, 4, 14, 4, 30, 2, 15, 4, 30, 2, 26, 2, 25, 6, 17, 2, 41, 3, 23, 4, 28, 2, 30, 4, 37, 4, 20, 2, 50, 2, 21, 6, 39, 4, 34, 2, 34, 4, 34, 2, 59, 2, 24, 6, 37, 4, 38, 2, 56, 5, 26, 2, 62, 4, 27, 4

Offset: 1

Valery A. Liskovets

T. D. Noe, Table of n, a(n) for n=1..1000
V. A. Liskovets and A. Mednykh, Number of non-orientable coverings of the Klein bottle
A. D. Mednykh, On the number of subgroups in the fundamental group of a closed surface, Commun. in Algebra, 16, No 10 (1988), 2137-2148.

Cf. A027842, A027844, A000005, A000203, A069733, A069734, A069735.

with(numtheory); A046524:=n->`if`(type(n/2, integer), (3*tau(n) + sigma(n/2) - tau(n/2))/2, tau(n)); seq(A046524(n), n=1..100); # Wesley Ivan Hurt, Feb 14 2014

kb[n_]:=If[OddQ[n],DivisorSigma[0,n],(3DivisorSigma[0,n]+ DivisorSigma[ 1,n/2]- DivisorSigma[0,n/2])/2]; Array[kb,90] (* Harvey P. Dale, Oct 08 2011 *)

def A046524(n) :
    f = lambda n : 1 if n % 2 == 1 else (n+7)//4
    return add(f(d) for d in divisors(n))
[A046524(n) for n in (1..87)] # Peter Luschny, Jul 23 2012

a(n)=d(n) (the number of divisors) for odd n.
a(n)=[3d(n)+sigma(n/2)-d(n/2)]/2 for even n where d(n) is the number and sigma(n) the sum of divisors of n (A000005 and A000203).
Inverse Moebius transform of 1, 2, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 6, 1, 6, 1, 7, 1, 7, ... . G.f.: Sum_{n>1} x^n*(1+2*x^n-x^(4*n)-x^(5*n))/(1+x^(2*n))/(1-x^(2*n))^2. - Vladeta Jovovic, Feb 03 2003

More terms from Vladeta Jovovic, Feb 03 2003

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

Original entry on oeis.org

1, 3, 5, 13, 7, 19, 9, 43, 18, 33, 13, 93, 15, 51, 35, 137, 19, 110, 21, 175, 45, 99, 25, 355, 38, 129, 58, 285, 31, 289, 33, 455, 65, 201, 63, 626, 39, 243, 75, 721, 43, 483, 45, 589, 126, 339, 49, 1305, 66, 498, 95, 783, 55, 750, 91, 1227

Offset: 1

N. J. A. Sloane, Oct 28 2015

nonn

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.

Cf. A263825-A263830, A263832.

A001001(n) = sumdiv(n, d, sigma(d) * d);
A007429(n) = sumdiv(n, d, sigma(d));
A007434(n) = sumdiv(n, d, moebius(n\d) * d^2);
A059376(n) = sumdiv(n, d, moebius(n\d) * d^3);
A060640(n) = sumdiv(n, d, sigma(n\d) * d);
EpiPcZn(n) = sumdiv(n, d, moebius(n\d) * d^2 * gcd(d,2));
S1(n)      = if (n%2, 0, A001001(n\2));
S11(n)     = A060640(n) - if(n%2, 0, A060640(n\2));
S21(n)     = if (n%2, 0, 2*A060640(n\2)) - if (n%4, 0, 2*A060640(n\4));
S22(n)     = { if (n%2, A060640(n), if (n%4, 0,
  sumdiv(n\4, d, 2*d*(sigma(n\(2*d)) - sigma(n\(4*d))))));
};
A027844(n) = S1(n) + S11(n) + S21(n);
a(n) = { 1/n * sumdiv(n, d,
  A059376(d) * S1(n\d) + EpiPcZn(d) * S21(n\d) + A007434(d) * S22(n\d));
};
vector(56, n, a(n))  \\ Gheorghe Coserea, May 04 2016

More terms from Gheorghe Coserea, May 04 2016

cp's OEIS Frontend

A046524 Number of coverings of Klein bottle with n lists.

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