A359289 Number of divisors of 4*n-2 of form 4*k+1.
1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 4, 1, 2, 2, 2, 2, 2, 1, 2, 3, 4, 1, 2, 1, 2, 3, 2, 1, 3, 1, 4, 2, 2, 2, 2, 2, 2, 3, 2, 1, 4, 1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 1, 2, 1, 2, 4, 2, 1, 2, 2, 4, 3, 2, 1, 4, 2, 2, 2, 2, 1, 4, 1, 3, 3, 2, 3, 2, 1
Offset: 1
Programs
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Mathematica
a[n_] := DivisorSum[4*n-2, 1 &, Mod[#, 4] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 16 2023 *)
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PARI
a(n) = sumdiv(4*n-2, d, d%4==1);
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PARI
my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(4*k-2)))) -
PARI
my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(4*k-3))))
Formula
a(n) = A001826(4*n-2).
G.f.: Sum_{k>0} x^k/(1 - x^(4*k-2)).
G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(4*k-3)).