A284281 - OEIS

%I #27 Nov 26 2023 03:11:47

%S 0,0,3,0,0,3,0,8,3,0,0,3,13,0,3,8,0,21,0,0,3,0,23,11,0,13,3,28,0,3,0,

%T 8,36,0,0,21,0,38,16,8,0,3,43,0,3,23,0,59,0,0,3,13,53,21,0,36,3,58,0,

%U 3,0,0,66,8,13,36,0,68,26,0,0,29,73,0,3,38,0,94,0,8

%N a(n) = Sum_{d|n, d == 3 (mod 5)} d.

%H Seiichi Manyama, <a href="/A284281/b284281.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=0} (5*k + 3)*x^(5*k+3)/(1 - x^(5*k+3)). - _Ilya Gutkovskiy_, Mar 25 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] == 3, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 24 2017 *)

%o (PARI) for(n=1, 82, print1(sumdiv(n, d, if(Mod(d, 5)==3, d, 0)),", ")) \\ _Indranil Ghosh_, Mar 24 2017

%o (Python)

%o from sympy import divisors

%o def a(n): return sum([d for d in divisors(n) if d%5==3]) # _Indranil Ghosh_, Mar 24 2017

%Y Cf. A013661, A109699, A284152.

%Y Cf. Sum_{d|n, d=k mod 5} d: A284097 (k=1), A284280 (k=2), this sequence (k=3), A284103 (k=4).

%K nonn,easy

%O 1,3

%A _Seiichi Manyama_, Mar 24 2017