A364209 - OEIS

%I #28 Jul 23 2023 13:03:54

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,1,2,1,1,

%T 1,2,1,1,1,2,1,1,1,2,1,1,1,2,2,1,1,2,1,1,1,3,1,1,1,2,1,1,2,2,1,1,1,2,

%U 1,2,1,2,1,1,1,2,2,1,1,2,1,1,1,3,1,1,1,2,1,1,2,2,1,1,1,2,1,2,1,3

%N Number of divisors of n of the form 3*k+1 that are at most sqrt(n).

%F G.f.: Sum_{k>=0} x^(3*k+1)^2 / (1 - x^(3*k+1)).

%t Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{1}, Mod[#, 3]] &)], {n, 100}]

%t nmax = 100; CoefficientList[Series[Sum[x^(3 k + 1)^2/(1 - x^(3 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A001817, A038548, A364357.

%K nonn

%O 1,16

%A _Ilya Gutkovskiy_, Jul 21 2023