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 A001842 #53 Jul 22 2025 15:50:40
%S A001842 0,0,0,1,0,0,1,1,0,1,0,1,1,0,1,2,0,0,1,1,0,2,1,1,1,0,0,2,1,0,2,1,0,2,
%T A001842 0,2,1,0,1,2,0,0,2,1,1,2,1,1,1,1,0,2,0,0,2,2,1,2,0,1,2,0,1,3,0,0,2,1,
%U A001842 0,2,2,1,1,0,0,3,1,2,2,1,0,2,0,1,2,0,1
%N A001842 Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).
%C A001842 Number of divisors of n of the form 4*k+3. - _Reinhard Zumkeller_, Apr 18 2006
%D A001842 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 132.
%D A001842 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 244.
%H A001842 T. D. Noe, <a href="/A001842/b001842.txt">Table of n, a(n) for n = 0..10000</a>
%H A001842 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>.
%H A001842 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 A001842 a(A072437(n)) = 0. - _Benoit Cloitre_, Apr 24 2003
%F A001842 a(n) = A001227(n) - A001826(n). - _Reinhard Zumkeller_, Apr 18 2006
%F A001842 G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(4*k)). - _Ilya Gutkovskiy_, Sep 11 2019
%F A001842 a(n) = Sum_{d|n} (binomial(d,3) mod 2). - _Ridouane Oudra_, Nov 19 2019
%F A001842 Sum_{k=1..n} a(k) = n*log(n)/4 + c*n + O(n^(1/3)*log(n)), where c = gamma(3,4) - (1 - gamma)/4 = A256846 - (1 - A001620)/4 = -0.180804... (Smith and Subbarao, 1981). - _Amiram Eldar_, Nov 25 2023
%p A001842 with(numtheory): seq(add(binomial(d,3) mod 2, d in divisors(n)), n=0..100); # _Ridouane Oudra_, Nov 19 2019
%t A001842 Join[{0}, Table[d = Divisors[n]; Length[Select[d, Mod[#, 4] == 3 &]], {n, 100}]] (* _T. D. Noe_, Aug 10 2012 *)
%t A001842 a[n_] := DivisorSum[n, 1 &, Mod[#, 4] == 3 &]; a[0] = 0; Array[a, 100, 0] (* _Amiram Eldar_, Nov 25 2023 *)
%o A001842 (PARI) a(n) = if(n<1, 0, sumdiv(n, d, d%4 == 3)); \\ _Amiram Eldar_, Nov 25 2023
%Y A001842 Cf. A001227, A001620, A001826, A072437, A256846.
%K A001842 nonn,easy
%O A001842 0,16
%A A001842 _N. J. A. Sloane_