|
%I #20 Nov 26 2023 06:34:43
%S 0,0,0,0,5,0,0,0,0,5,0,12,0,0,5,0,0,0,19,5,0,0,0,12,5,26,0,0,0,5,0,0,
%T 33,0,5,12,0,19,0,45,0,0,0,0,5,0,47,12,0,5,0,26,0,54,5,0,19,0,0,17,61,
%U 0,0,0,5,33,0,68,0,5,0,12,0,0,80,19,0,26,0,45,0,82
%N a(n) = Sum_{d|n, d == 5 (mod 7)} d.
%H Robert Israel, <a href="/A284446/b284446.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=0} (5+7k) x^(5+7k)/(1-x^(5+7k)). - _Robert Israel_, Mar 27 2017
%F 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
%p f:= n -> convert(select(t -> t mod 7 = 5, numtheory:-divisors(n)),`+`):
%p map(f, [$1..1000]); # _Robert Israel_, Mar 27 2017
%t Table[DivisorSum[n, # &, Mod[#, 7] == 5 &], {n, 82}] (* _Giovanni Resta_, Mar 27 2017 *)
%o (PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 7)==5, d, 0)), ", ")) \\ _Indranil Ghosh_, Mar 27 2017
%Y Cf. A109707.
%Y Cf. Sum_{d|n, d == k (mod 7)} d: A284099 (k=1), A284443 (k=2), A284444 (k=3), A284445 (k=4), this sequence (k=5), A284105 (k=6).
%K nonn,easy
%O 1,5
%A _Seiichi Manyama_, Mar 27 2017
|
