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%I #23 Nov 26 2023 03:10:43
%S 1,1,1,1,1,7,1,1,1,1,12,7,1,1,1,17,1,7,1,1,22,12,1,7,1,27,1,1,1,7,32,
%T 17,12,1,1,43,1,1,1,1,42,28,1,12,1,47,1,23,1,1,52,27,1,7,12,57,1,1,1,
%U 7,62,32,22,17,1,84,1,1,1,1,72,43,1,1,1,77,12,33,1
%N a(n) = Sum_{d|n, d == 1 (mod 5)} d.
%H Seiichi Manyama, <a href="/A284097/b284097.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=0} (5*k + 1)*x^(5*k+1)/(1 - x^(5*k+1)). - _Ilya Gutkovskiy_, Mar 21 2017
%F Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/60 = 0.164493... (A013661 / 10). - _Amiram Eldar_, Nov 26 2023
%t Table[Sum[If[Mod[d, 5] == 1, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 21 2017 *)
%o (PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 5)==1, d, 0)), ", ")) \\ _Indranil Ghosh_, Mar 21 2017
%o (Python)
%o from sympy import divisors
%o def a(n): return sum([d for d in divisors(n) if d%5==1]) # _Indranil Ghosh_, Mar 21 2017
%Y Cf. A013661, A109697.
%Y Cf. Sum_{d|n, d=1 mod k} d: A000593 (k=2), A078181 (k=3), A050449 (k=4), this sequence (k=5), A284098 (k=6), A284099 (k=7), A284100 (k=8).
%K nonn,easy
%O 1,6
%A _Seiichi Manyama_, Mar 20 2017
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