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A293903 Sum of proper divisors of n of the form 4k+3.

%I A293903 #17 Nov 27 2023 03:04:49
%S A293903 0,0,0,0,0,3,0,0,3,0,0,3,0,7,3,0,0,3,0,0,10,11,0,3,0,0,3,7,0,18,0,0,
%T A293903 14,0,7,3,0,19,3,0,0,10,0,11,18,23,0,3,7,0,3,0,0,30,11,7,22,0,0,18,0,
%U A293903 31,10,0,0,14,0,0,26,42,0,3,0,0,18,19,18,42,0,0,30,0,0,10,0,43,3,11,0,18,7,23,34,47,19,3,0,7,14,0,0,54,0,0,60
%N A293903 Sum of proper divisors of n of the form 4k+3.
%H A293903 Antti Karttunen, <a href="/A293903/b293903.txt">Table of n, a(n) for n = 1..16384</a>
%H A293903 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.
%F A293903 a(n) = Sum_{d|n, d<n} [3 == d mod 4]*d.
%F A293903 a(n) = A091570(n) - A293901(n).
%F A293903 G.f.: Sum_{k>=1} (4*k-1) * x^(8*k-2) / (1 - x^(4*k-1)). - _Ilya Gutkovskiy_, Apr 14 2021
%F A293903 Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/48 - 1/8 = 0.0806167... . - _Amiram Eldar_, Nov 27 2023
%t A293903 Array[DivisorSum[#, # &, Mod[#, 4] == 3 &] - Boole[Mod[#, 4] == 3] # &, 105] (* _Michael De Vlieger_, Oct 23 2017 *)
%o A293903 (PARI) A293903(n) = sumdiv(n,d,(d<n)*(3==(d%4))*d);
%Y A293903 Cf. A050452, A091570, A293513, A293901.
%K A293903 nonn,easy
%O A293903 1,6
%A A293903 _Antti Karttunen_, Oct 19 2017