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 A320015 #15 Nov 25 2023 08:00:35
%S A320015 0,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,1,1,1,2,2,2,1,1,2,2,1,2,1,2,1,1,2,2,
%T A320015 3,1,1,2,2,2,1,2,1,2,2,2,1,1,2,3,2,2,1,1,3,2,2,2,1,2,1,2,2,1,3,2,1,2,
%U A320015 2,4,1,1,1,2,3,2,3,2,1,2,1,2,1,2,3,2,2,2,1,2,3,2,2,2,3,1,1,3,2,3,1,2,1,2,4
%N A320015 Number of proper divisors of n that are either of the form 6*k+1 or 6*k + 5.
%H A320015 Antti Karttunen, <a href="/A320015/b320015.txt">Table of n, a(n) for n = 1..65537</a>
%H A320015 R. A. Smith and M. V. Subbarao, <a href="https://doi.org/10.4153/CMB-1981-005-3">The average number of divisors in an arithmetic progression</a>, Canadian Mathematical Bulletin, Vol. 24, No. 1 (1981), pp. 37-41.
%F A320015 a(n) = A320001(n) + A320005(n).
%F A320015 a(n) = A035218(n) - ch15(n), where ch15 is the characteristic function of numbers of the form +-1 mod 6, i.e., ch15(n) = A232991(n-1).
%F A320015 Sum_{k=1..n} a(k) = n*log(n)/3 + c*n + O(n^(1/3)*log(n)), where c = 2*(gamma + log(12)/4 - 1)/3 = 0.132294..., and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - _Amiram Eldar_, Nov 25 2023
%t A320015 a[n_] := DivisorSum[n, 1 &, # < n && MemberQ[{1, 5}, Mod[#, 6]] &]; Array[a, 100] (* _Amiram Eldar_, Nov 25 2023 *)
%o A320015 (PARI) A320015(n) = if(!n,n,sumdiv(n, d, (d<n)&&(d%2)&&(d%3)));
%Y A320015 Cf. A001620, A035218, A232991, A293895, A293896, A320001, A320005.
%K A320015 nonn,easy
%O A320015 1,10
%A A320015 _Antti Karttunen_, Oct 03 2018