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A284105 a(n) = Sum_{d|n, d == 6 (mod 7)} d.

%I A284105 #19 Nov 26 2023 06:34:55
%S A284105 0,0,0,0,0,6,0,0,0,0,0,6,13,0,0,0,0,6,0,20,0,0,0,6,0,13,27,0,0,6,0,0,
%T A284105 0,34,0,6,0,0,13,20,41,6,0,0,0,0,0,54,0,0,0,13,0,33,55,0,0,0,0,26,0,
%U A284105 62,0,0,13,6,0,34,69,0,0,6,0,0,0,76,0,19,0,20,27,41
%N A284105 a(n) = Sum_{d|n, d == 6 (mod 7)} d.
%H A284105 Seiichi Manyama, <a href="/A284105/b284105.txt">Table of n, a(n) for n = 1..10000</a>
%F A284105 G.f.: Sum_{k>=1} (7*k - 1)*x^(7*k-1)/(1 - x^(7*k-1)). - _Ilya Gutkovskiy_, Mar 21 2017
%F A284105 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 A284105 Table[Sum[If[Mod[d,7] == 6,d, 0], {d, Divisors[n]}], {n, 82}] (* _Indranil Ghosh_, Mar 21 2017 *)
%o A284105 (PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d,7)==6, d, 0)),", ")) \\ _Indranil Ghosh_, Mar 21 2017
%o A284105 (Python)
%o A284105 from sympy import divisors
%o A284105 def a(n): return sum([d for d in divisors(n) if d%7==6]) # _Indranil Ghosh_, Mar 21 2017
%Y A284105 Cf. A109708.
%Y A284105 Cf. Sum_{d|n, d == k-1 (mod k)} d: A000593 (k=2), A078182 (k=3), A050452 (k=4), A284103 (k=5), A284104 (k=6), this sequence (k=7).
%Y A284105 Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), A284444 (k=3), A284445 (k=4), A284446 (k=5), this sequence (k=6).
%K A284105 nonn,easy
%O A284105 1,6
%A A284105 _Seiichi Manyama_, Mar 20 2017