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%I #19 Aug 16 2023 02:26:45
%S 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,
%T 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,
%U 2,1,2,2,4,3,2,1,4,2,2,2,2,1,4,1,3,3,2,3,2,1
%N Number of divisors of 4*n-2 of form 4*k+1.
%F a(n) = A001826(4*n-2).
%F G.f.: Sum_{k>0} x^k/(1 - x^(4*k-2)).
%F G.f.: Sum_{k>0} x^(2*k-1)/(1 - x^(4*k-3)).
%t a[n_] := DivisorSum[4*n-2, 1 &, Mod[#, 4] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Aug 16 2023 *)
%o (PARI) a(n) = sumdiv(4*n-2, d, d%4==1);
%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(4*k-2))))
%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(2*k-1)/(1-x^(4*k-3))))
%Y Cf. A001826, A078703, A359227.
%K nonn,easy
%O 1,3
%A _Seiichi Manyama_, Dec 24 2022