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 A363854 #17 Jun 25 2023 09:42:20 %S A363854 0,1,0,1,0,1,0,2,0,1,0,1,0,2,0,1,1,1,0,2,0,1,0,1,0,3,0,1,0,2,0,2,0,1, %T A363854 1,1,0,2,0,1,0,1,1,3,0,2,0,1,0,2,0,1,1,1,0,3,0,1,0,1,0,4,0,1,0,2,0,2, %U A363854 1,1,1,1,0,2,0,1,0,2,0,3,0,2,0,1,0,3,0,1,2,1,0,2,0,2,1,1,0,3,0,1 %N A363854 Number of divisors of 7*n-2 of form 7*k+6. %C A363854 Also number of divisors of 7*n-2 of form 7*k+2. %F A363854 a(n) = A363795(7*n-2) = A363808(7*n-2). %F A363854 G.f.: Sum_{k>0} x^(2*k)/(1 - x^(7*k-1)). %F A363854 G.f.: Sum_{k>0} x^(6*k-4)/(1 - x^(7*k-5)). %t A363854 a[n_] := DivisorSum[7*n - 2, 1 &, Mod[#, 7] == 6 &]; Array[a, 100] (* _Amiram Eldar_, Jun 25 2023 *) %o A363854 (PARI) a(n) = sumdiv(7*n-2, d, d%7==6); %Y A363854 Cf. A361691, A363855, A363856, A363857, A363858. %Y A363854 Cf. A363795, A363808. %K A363854 nonn %O A363854 1,8 %A A363854 _Seiichi Manyama_, Jun 24 2023