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A050461 a(n) = Sum_{d|n, n/d=1 mod 4} d^2.

%I A050461 #26 Nov 06 2023 02:15:49
%S A050461 1,4,9,16,26,36,49,64,82,104,121,144,170,196,234,256,290,328,361,416,
%T A050461 442,484,529,576,651,680,738,784,842,936,961,1024,1090,1160,1274,1312,
%U A050461 1370,1444,1530,1664,1682,1768,1849,1936,2132,2116,2209
%N A050461 a(n) = Sum_{d|n, n/d=1 mod 4} d^2.
%C A050461 Not multiplicative: a(3)*a(7) <> a(21), for example. - _R. J. Mathar_, Dec 20 2011
%H A050461 Reinhard Zumkeller, <a href="/A050461/b050461.txt">Table of n, a(n) for n = 1..10000</a>
%F A050461 a(n) = A050470(n) + A050465(n). - _Reinhard Zumkeller_, Mar 06 2012
%F A050461 From _Amiram Eldar_, Nov 05 2023: (Start)
%F A050461 a(n) = A076577(n) - A050465(n).
%F A050461 a(n) = (A050470(n) + A076577(n))/2.
%F A050461 Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = Pi^3/64 + 7*zeta(3)/16 = 1.010372968262... . (End)
%p A050461 A050461 := proc(n)
%p A050461         a := 0 ;
%p A050461         for d in numtheory[divisors](n) do
%p A050461                 if (n/d) mod 4 = 1 then
%p A050461                         a := a+d^2 ;
%p A050461                 end if;
%p A050461         end do:
%p A050461         a;
%p A050461 end proc:
%p A050461 seq(A050461(n),n=1..40) ; # _R. J. Mathar_, Dec 20 2011
%t A050461 a[n_] := DivisorSum[n, Boole[Mod[n/#, 4] == 1]*#^2&]; Array[a, 50] (* _Jean-François Alcover_, Feb 12 2018 *)
%o A050461 (Haskell)
%o A050461 a050461 n = sum [d ^ 2 | d <- a027750_row n, mod (div n d) 4 == 1]
%o A050461 -- _Reinhard Zumkeller_, Mar 06 2012
%o A050461 (PARI) a(n) = sumdiv(n, d, (n/d % 4 == 1) * d^2); \\ _Amiram Eldar_, Nov 05 2023
%Y A050461 Cf. A050465, A050470, A076577, A027750, A002117.
%Y A050461 Cf. A050460, A050462, A050463.
%K A050461 nonn,easy
%O A050461 1,2
%A A050461 _N. J. A. Sloane_, Dec 23 1999