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%I #47 Nov 25 2023 04:44:17
%S 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 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 0,2,2,1,1,0,0,3,1,2,2,1,0,2,0,1,2,0,1
%N Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).
%C Number of divisors of n of the form 4*k+3. - _Reinhard Zumkeller_, Apr 18 2006
%H T. D. Noe, <a href="/A001842/b001842.txt">Table of n, a(n) for n = 0..10000</a>
%H Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>.
%H 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 a(A072437(n)) = 0. - _Benoit Cloitre_, Apr 24 2003
%F a(n) = A001227(n) - A001826(n). - _Reinhard Zumkeller_, Apr 18 2006
%F G.f.: Sum_{k>=1} x^(3*k)/(1 - x^(4*k)). - _Ilya Gutkovskiy_, Sep 11 2019
%F a(n) = Sum_{d|n} (binomial(d,3) mod 2). - _Ridouane Oudra_, Nov 19 2019
%F 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 with(numtheory): seq(add(binomial(d,3) mod 2, d in divisors(n)), n=0..100); # _Ridouane Oudra_, Nov 19 2019
%t Join[{0}, Table[d = Divisors[n]; Length[Select[d, Mod[#, 4] == 3 &]], {n, 100}]] (* _T. D. Noe_, Aug 10 2012 *)
%t a[n_] := DivisorSum[n, 1 &, Mod[#, 4] == 3 &]; a[0] = 0; Array[a, 100, 0] (* _Amiram Eldar_, Nov 25 2023 *)
%o (PARI) a(n) = if(n<1, 0, sumdiv(n, d, d%4 == 3)); \\ _Amiram Eldar_, Nov 25 2023
%Y Cf. A001227, A001620, A001826, A072437, A256846.
%K nonn,easy
%O 0,16
%A _N. J. A. Sloane_
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