A284103 - OEIS

%I #24 Sep 24 2024 16:30:43

%S 0,0,0,4,0,0,0,4,9,0,0,4,0,14,0,4,0,9,19,4,0,0,0,28,0,0,9,18,29,0,0,4,

%T 0,34,0,13,0,19,39,4,0,14,0,48,9,0,0,28,49,0,0,4,0,63,0,18,19,29,59,4,

%U 0,0,9,68,0,0,0,38,69,14,0,37,0,74,0,23,0,39,79

%N a(n) = Sum_{d|n, d == 4 (mod 5)} d.

%H Seiichi Manyama, <a href="/A284103/b284103.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=1} (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] == 4, d, 0], {d, Divisors[n]}], {n, 79}] (* _Indranil Ghosh_, Mar 21 2017 *)

%t Table[Total[Select[Divisors[n],Mod[#,5]==4&]],{n,80}] (* _Harvey P. Dale_, Sep 24 2024 *)

%o (PARI) for(n=1, 79, print1(sumdiv(n, d, if(Mod(d, 5)==4, 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==4]) # _Indranil Ghosh_, Mar 21 2017

%Y Cf. A013661, A109700.

%Y Cf. Sum_{d|n, d=k-1 mod k} d: A000593 (k=2), A078182 (k=3), A050452 (k=4), this sequence (k=5), A284104 (k=6), A284105 (k=7).

%K nonn,easy

%O 1,4

%A _Seiichi Manyama_, Mar 20 2017