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a[n_] := DivisorSum[5*n - 3, # &, Mod[#, 5] == 1 &]; Array[a, 100] (* Amiram Eldar, Jul 17 2023 *)
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G.f.: Sum_{k>0} (5*k-4) * x^(2*k-1) / (1 - x^(5*k-4)).