A359212 Number of divisors of 3*n-2 of form 3*k+1.
1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 3, 4, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2, 2, 4, 4, 2, 2, 5, 2, 2, 2, 6, 2, 2, 2, 4, 2, 4, 4, 4, 2, 2, 2, 4, 2, 4, 2, 6, 2, 2, 3, 4, 4, 2, 2, 4, 2, 4, 2, 6, 2, 2, 2, 6, 2, 2, 4, 6, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 5, 4, 2, 2, 4
Offset: 1
Programs
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Mathematica
a[n_] := DivisorSum[3*n-2, 1 &, Mod[#, 3] == 1 &]; Array[a, 100] (* Amiram Eldar, Aug 23 2023 *)
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PARI
a(n) = sumdiv(3*n-2, d, d%3==1);
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PARI
my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(3*k-2))))
Formula
G.f.: Sum_{k>0} x^k/(1 - x^(3*k-2)).