OFFSET
1,17
LINKS
C. H. Kim and J. K. Koo, Estimation of Genus for Certain Arithmetic Groups, Communications in Algebra, 32:7 (2004), 2479-2495.
MATHEMATICA
A000003[n_] :=
Length[Select[
Flatten[#, 1] &@
Table[{i, j, (j^2 + 4 n)/(4 i)}, {i, Sqrt[4 n/3]}, {j, 1 - i, i}],
Mod[#3, 1] == 0 && #3 >= # &&
GCD[##] == 1 && ! (# == #3 && #2 < 0) & @@ # &]];
A001617[n_] :=
If[n < 1, 0,
1 + Sum[MoebiusMu[d]^2 n/d/12 - EulerPhi[GCD[d, n/d]]/2, {d,
Divisors@n}] -
Count[(#^2 - # + 1)/n & /@ Range[n], _?IntegerQ]/3 -
Count[(#^2 + 1)/n & /@ Range[n], _?IntegerQ]/4];
A029937[n_] =
If[n < 5, 0,
1 + Sum[d^2*MoebiusMu[n/d]/24 - EulerPhi[d]*EulerPhi[n/d]/4, {d,
Divisors[n]}]];
A276183[n_] :=
If[0 <= n <= 4,
0, (A001617[n] + 1)/2 -
If[Mod[n, 8] == 3, 4, If[Mod[n, 8] == 7, 6, 3]]*A000003[n]/12];
CROSSREFS
KEYWORD
nonn
AUTHOR
David Jao, Aug 23 2023
STATUS
approved