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 A083913 #13 Dec 30 2023 05:11:54
%S A083913 0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0,2,0,
%T A083913 0,1,0,0,2,0,0,1,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,2,0,1,2,0,0,
%U A083913 2,0,0,1,1,0,1,0,0,2,0,0,1,0,1,1,0,1,1,0,0,1,1,1,2,0,0,1,0,0,2,0,0,1,1,1,1
%N A083913 Number of divisors of n that are congruent to 3 modulo 10.
%H A083913 Amiram Eldar, <a href="/A083913/b083913.txt">Table of n, a(n) for n = 1..10000</a>
%H A083913 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 A083913 a(n) = A000005(n) - A083910(n) - A083911(n) - A083912(n) - A083914(n) - A083915(n) - A083916(n) - A083917(n) - A083918(n) - A083919(n).
%F A083913 G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(10*k)). - _Ilya Gutkovskiy_, Sep 11 2019
%F A083913 Sum_{k=1..n} a(k) = n*log(n)/10 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,10) - (1 - gamma)/10 = 0.07771547..., gamma(3,10) = -(psi(3/10) + log(10))/10 is a generalized Euler constant, and gamma is Euler's constant (A001620) (Smith and Subbarao, 1981). - _Amiram Eldar_, Dec 30 2023
%t A083913 a[n_] := DivisorSum[n, 1 &, Mod[#, 10] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Dec 30 2023 *)
%o A083913 (PARI) a(n) = sumdiv(n, d, d % 10 == 3); \\ _Amiram Eldar_, Dec 30 2023
%Y A083913 Cf. A000005, A001227, A010879.
%Y A083913 Cf. A001620, A002392, A354642 (psi(3/10)).
%Y A083913 Cf. A083910, A083911, A083912, A083914, A083915, A083916, A083917, A083918, A083919.
%K A083913 nonn,easy
%O A083913 1,33
%A A083913 _Reinhard Zumkeller_, May 08 2003