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A284099 a(n) = Sum_{d|n, d == 1 (mod 7)} d.

%I A284099 #30 Nov 26 2023 06:34:40
%S A284099 1,1,1,1,1,1,1,9,1,1,1,1,1,1,16,9,1,1,1,1,1,23,1,9,1,1,1,1,30,16,1,9,
%T A284099 1,1,1,37,1,1,1,9,1,1,44,23,16,1,1,9,1,51,1,1,1,1,1,9,58,30,1,16,1,1,
%U A284099 1,73,1,23,1,1,1,1,72,45,1,1,16,1,1,79,1,9,1,1
%N A284099 a(n) = Sum_{d|n, d == 1 (mod 7)} d.
%H A284099 Seiichi Manyama, <a href="/A284099/b284099.txt">Table of n, a(n) for n = 1..10000</a>
%F A284099 G.f.: Sum_{k>=0} (7*k + 1)*x^(7*k+1)/(1 - x^(7*k+1)). - _Ilya Gutkovskiy_, Mar 21 2017
%F A284099 G.f.: Sum_{n >= 1} x^n*(1 + 6*x^(7*n))/(1 - x^(7*n))^2. - _Peter Bala_, Dec 19 2021
%F A284099 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 A284099 Table[Sum[If[Mod[d, 7] == 1, d, 0], {d, Divisors[n]}], {n, 82}] (* _Indranil Ghosh_, Mar 21 2017 *)
%t A284099 Table[DivisorSum[n,#&,Mod[#,7]==1&],{n,90}] (* _Harvey P. Dale_, Aug 08 2021 *)
%o A284099 (PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 7)==1, d, 0)), ", ")) \\ _Indranil Ghosh_, Mar 21 2017
%o A284099 (Python)
%o A284099 from sympy import divisors
%o A284099 def a(n): return sum([d for d in divisors(n) if d%7==1]) # _Indranil Ghosh_, Mar 21 2017
%Y A284099 Cf. A109703.
%Y A284099 Cf. Sum_{d|n, d == 1 (mod k)} d: A000593 (k=2), A078181 (k=3), A050449 (k=4), A284097 (k=5), A284098 (k=6), this sequence (k=7), A284100 (k=8).
%Y A284099 Cf. Sum_{d|n, d == k (mod 7)} d: this sequence (k=1), A284443 (k=2), A284444 (k=3), A284445 (k=4), A284446 (k=5), A284105 (k=6).
%K A284099 nonn,easy
%O A284099 1,8
%A A284099 _Seiichi Manyama_, Mar 20 2017