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A263827
The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.
2
2, 6, 10, 14, 14, 30, 18, 30, 36, 42, 26, 70, 30, 54, 70, 62, 38, 108, 42, 98, 90, 78, 50, 150, 76, 90, 116, 126, 62, 210, 66, 126, 130, 114, 126, 252, 78, 126, 150, 210, 86, 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
OFFSET
1,1
LINKS
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.
MAPLE
A263827 := proc(n)
local locn, a, twol, fourl ;
locn := 2*n ;
# Theorem 3 (iii)
a := 0 ;
for twol in numtheory[divisors](locn) do
if type(twol, 'even') then
a := a+numtheory[sigma](locn/twol) ;
end if;
end do:
for fourl in numtheory[divisors](locn) do
if modp(fourl, 4) = 0 then
a := a-numtheory[sigma](locn/fourl) ;
end if;
end do:
%*2 ;
end proc: # R. J. Mathar, Nov 03 2015
MATHEMATICA
a[n_] := 2*Sum[If[Mod[d, 4] == 2, DivisorSigma[1, 2*n/d], 0], {d, Divisors[ 2*n ] } ];
Array[a, 70] (* Jean-François Alcover, Dec 03 2017 *)
PROG
(PARI)
A007429(n) = sumdiv(n, d, sigma(d));
a(n) = 2*A007429(n) - if(n%2, 0, 2*A007429(n\2));
vector(70, n, a(n)) \\ Gheorghe Coserea, May 04 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 28 2015
STATUS
approved