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A284444 a(n) = Sum_{d|n, d == 3 (mod 7)} d.

%I A284444 #19 Nov 26 2023 06:34:49
%S A284444 0,0,3,0,0,3,0,0,3,10,0,3,0,0,3,0,17,3,0,10,3,0,0,27,0,0,3,0,0,13,31,
%T A284444 0,3,17,0,3,0,38,3,10,0,3,0,0,48,0,0,27,0,10,20,52,0,3,0,0,3,0,59,13,
%U A284444 0,31,3,0,0,69,0,17,3,10,0,27,73,0,3,38,0,3,0,90,3
%N A284444 a(n) = Sum_{d|n, d == 3 (mod 7)} d.
%H A284444 Seiichi Manyama, <a href="/A284444/b284444.txt">Table of n, a(n) for n = 1..10000</a>
%F A284444 G.f.: Sum_{k>=0} (7*k + 3)*x^(7*k+3)/(1 - x^(7*k+3)). - _Ilya Gutkovskiy_, Mar 28 2017
%F A284444 Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/84 = 0.117495... . - _Amiram Eldar_, Nov 26 2023
%t A284444 Table[Sum[If[Mod[d, 7] == 3, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A284444 (PARI) a(n) = sumdiv(n, d, d*((d % 7) == 3)); \\ _Amiram Eldar_, Nov 26 2023
%Y A284444 Cf. A109705.
%Y A284444 Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), this sequence (k=3), A284445 (k=4), A284446 (k=5), A284105 (k=6).
%K A284444 nonn,easy
%O A284444 1,3
%A A284444 _Seiichi Manyama_, Mar 27 2017