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%I #34 Nov 26 2023 03:06:53
%S 0,0,3,0,0,3,7,0,3,0,11,3,0,7,18,0,0,3,19,0,10,11,23,3,0,0,30,7,0,18,
%T 31,0,14,0,42,3,0,19,42,0,0,10,43,11,18,23,47,3,7,0,54,0,0,30,66,7,22,
%U 0,59,18,0,31,73,0,0,14,67,0,26,42,71,3,0,0,93,19,18
%N a(n) = Sum_{d|n, d == 3 (mod 4)} d.
%H Seiichi Manyama, <a href="/A050452/b050452.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale)
%H Mariusz Skałba, <a href="http://math.colgate.edu/~integers/u92/u92.pdf">A Note on Sums of Two Squares and Sum-of-divisors Functions</a>, INTEGERS 20A (2020) A92.
%F a(n) = A000593(n) - A050449(n). - _Reinhard Zumkeller_, Apr 18 2006
%F G.f.: Sum_{k>=1} (4*k - 1)*x^(4*k-1)/(1 - x^(4*k-1)). - _Ilya Gutkovskiy_, Mar 21 2017
%F Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/48 = 0.205616... (A245058). - _Amiram Eldar_, Nov 26 2023
%p A050452 := proc(n)
%p a := 0 ;
%p for d in numtheory[divisors](n) do
%p if d mod 4 = 3 then
%p a := a+d ;
%p end if;
%p end do:
%p a;
%p end proc:
%p seq(A050452(n),n=1..40) ; # _R. J. Mathar_, Dec 20 2011
%t Table[Total[Select[Divisors[n],Mod[#,4]==3&]],{n,80}] (* _Harvey P. Dale_, Jul 07 2013 *)
%o (PARI) a(n) = sumdiv(n, d, d*((d % 4) == 3)); \\ _Amiram Eldar_, Nov 26 2023
%Y Cf. A000593, A050449, A001842, A035462, A245058.
%Y Cf. Sum_{d|n, d=k-1 mod k} d: A000593 (k=2), A078182 (k=3), this sequence (k=4).
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Dec 23 1999
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