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A284443 a(n) = Sum_{d|n, d == 2 (mod 7)} d.

%I A284443 #21 Nov 26 2023 06:34:52
%S A284443 0,2,0,2,0,2,0,2,9,2,0,2,0,2,0,18,0,11,0,2,0,2,23,2,0,2,9,2,0,32,0,18,
%T A284443 0,2,0,11,37,2,0,2,0,2,0,46,9,25,0,18,0,2,51,2,0,11,0,2,0,60,0,32,0,2,
%U A284443 9,18,65,2,0,2,23,2,0,83,0,39,0,2,0,2,79,18,9
%N A284443 a(n) = Sum_{d|n, d == 2 (mod 7)} d.
%H A284443 Seiichi Manyama, <a href="/A284443/b284443.txt">Table of n, a(n) for n = 1..10000</a>
%F A284443 G.f.: Sum_{k>=0} (7*k + 2)*x^(7*k+2)/(1 - x^(7*k+2)). - _Ilya Gutkovskiy_, Mar 28 2017
%F A284443 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 A284443 Table[Sum[If[Mod[d, 7] == 2, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 27 2017 *)
%o A284443 (PARI) a(n) = sumdiv(n, d, d*((d % 7) == 2)); \\ _Amiram Eldar_, Nov 26 2023
%Y A284443 Cf. A109704.
%Y A284443 Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), this sequence (k=2), A284444 (k=3), A284445 (k=4), A284446 (k=5), A284105 (k=6).
%K A284443 nonn,easy
%O A284443 1,2
%A A284443 _Seiichi Manyama_, Mar 27 2017