A284361 - OEIS

%I #26 Apr 12 2024 04:37:08

%S 1,1,1,5,6,7,1,5,10,16,12,11,1,15,21,21,1,16,20,40,22,12,1,35,31,27,

%T 10,19,30,67,32,21,12,35,41,56,1,20,40,80,42,42,1,60,75,47,1,51,50,91,

%U 52,31,1,70,72,75,20,30,60,151,62,32,31,85,71,84,1,39,70,135

%N a(n) = Sum_{d|n, d = 0, 1, or 4 mod 5} d.

%H Seiichi Manyama, <a href="/A284361/b284361.txt">Table of n, a(n) for n = 1..10000</a>

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Pi^2/20 = A102753 / 10 = 0.4934802... . - _Amiram Eldar_, Apr 12 2024

%t Table[Sum[If[Mod[d, 5]<2 || Mod[d, 5]==4, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 25 2017 *)

%t Table[Total[Select[Divisors[n],MemberQ[{0,1,4},Mod[#,5]]&]],{n,70}] (* _Harvey P. Dale_, Aug 02 2020 *)

%o (PARI) a(n) = sumdiv(n, d, ((d + 1) % 5 < 3) * d); \\ _Amiram Eldar_, Apr 12 2024

%Y Cf. A036820 (1/f(-x, -x^4)), A113429 (f(-x, -x^4)), A102753.

%Y Cf. Sum_{d|n, d = 0, 1, or k-1 mod k} d: A000203 (k=3), this sequence (k=5), A284362 (k=6), A284363 (k=7), A284372 (k=12).

%K nonn

%O 1,4

%A _Seiichi Manyama_, Mar 25 2017