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A050464 a(n) = Sum_{d|n, n/d=3 mod 4} d.

%I A050464 #28 Nov 06 2023 02:16:53
%S A050464 0,0,1,0,0,2,1,0,3,0,1,4,0,2,6,0,0,6,1,0,10,2,1,8,0,0,10,4,0,12,1,0,
%T A050464 14,0,6,12,0,2,14,0,0,20,1,4,18,2,1,16,7,0,18,0,0,20,6,8,22,0,1,24,0,
%U A050464 2,31,0,0,28,1,0,26,12,1,24,0,0,31,4,18,28,1,0,30,0,1
%N A050464 a(n) = Sum_{d|n, n/d=3 mod 4} d.
%H A050464 Seiichi Manyama, <a href="/A050464/b050464.txt">Table of n, a(n) for n = 1..10000</a>
%F A050464 G.f.: Sum_{k>=1} k*x^(3*k)/(1 - x^(4*k)). - _Ilya Gutkovskiy_, Sep 13 2019
%F A050464 G.f.: Sum_{k>0} x^(4*k-1) / (1 - x^(4*k-1))^2. - _Seiichi Manyama_, Jun 29 2023
%F A050464 from _Amiram Eldar_, Nov 05 2023: (Start)
%F A050464 a(n) = A002131(n) - A050460(n).
%F A050464 a(n) = A050460(n) - A050469(n).
%F A050464 a(n) = (A002131(n) - A050469(n))/2.
%F A050464 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A247037. (End)
%t A050464 a[n_] := DivisorSum[n, # &, Mod[n/#, 4] == 3 &]; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)
%o A050464 (PARI) a(n)={sumdiv(n, d, d*(n/d%4==3))} \\ _Andrew Howroyd_, Sep 13 2019
%Y A050464 Cf. A002131, A050460, A050469, A247037, A326400, A363900.
%Y A050464 Cf. A050465, A050466, A050467.
%K A050464 nonn,easy
%O A050464 1,6
%A A050464 _N. J. A. Sloane_, Dec 23 1999
%E A050464 Offset changed to 1 by _Ilya Gutkovskiy_, Sep 13 2019