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

1,2

Links

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.

Formula

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

Maple

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

Mathematica

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 *)

Prog

(Sage)
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

Crossrefs

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

Sequence in context: A358536 A274457 A328579 * A086571 A350509 A133945

Adjacent sequences: A046521 A046522 A046523 * A046525 A046526 A046527

Keyword

nonn,easy,nice

Author

Valery A. Liskovets

Extensions

More terms from Vladeta Jovovic, Feb 03 2003

Status

approved