This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A359305 #21 Dec 27 2022 07:08:28
%S A359305 1,1,1,1,1,2,1,1,1,1,2,1,2,1,1,2,1,1,1,2,2,1,1,2,1,2,2,1,1,1,2,1,1,2,
%T A359305 2,2,2,1,1,1,3,1,1,1,1,3,1,2,1,2,2,1,1,2,2,2,2,1,1,1,2,2,2,1,1,2,1,2,
%U A359305 2,1,3,1,2,1,1,4,1,1,2,1,2,1,2,1,1,2,1,2,2,3
%N A359305 Number of divisors of 6*n-1 of form 6*k+1.
%C A359305 Also number of divisors of 6*n-1 of form 6*k+5.
%H A359305 Seiichi Manyama, <a href="/A359305/b359305.txt">Table of n, a(n) for n = 1..10000</a>
%F A359305 a(n) = A279060(6*n-1) = A319995(6*n-1).
%F A359305 G.f.: Sum_{k>0} x^k/(1 - x^(6*k-1)).
%F A359305 G.f.: Sum_{k>0} x^(5*k-4)/(1 - x^(6*k-5)).
%F A359305 From _Amiram Eldar_, Dec 26 2022: (Start)
%F A359305 a(n) = A000005(A016969(n-1))/2.
%F A359305 Sum_{k=1..n} a(k) = (log(n) + 2*gamma - 1 + 3*log(2) + 2*log(3))*n/6 + O(n^(1/3)*log(n)), where gamma is Euler's constant (A001620). (End)
%t A359305 a[n_] := DivisorSigma[0, 6*n - 1]/2; Array[a, 100] (* _Amiram Eldar_, Dec 26 2022 *)
%o A359305 (PARI) a(n) = sumdiv(6*n-1, d, d%6==1);
%o A359305 (PARI) a(n) = sumdiv(6*n-1, d, d%6==5);
%o A359305 (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-x^(6*k-1))))
%o A359305 (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=1, N, x^(5*k-4)/(1-x^(6*k-5))))
%Y A359305 Cf. A279060, A319995.
%Y A359305 Cf. A000005, A001620, A016969, A078703, A359211, A359233.
%Y A359305 Cf. A359306, A359307, A359308, A359309.
%Y A359305 Cf. A359324, A359325, A359326, A359327.
%K A359305 nonn,easy
%O A359305 1,6
%A A359305 _Seiichi Manyama_, Dec 25 2022