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Number of divisors of n of the form 5*k+1 that are at most sqrt(n).
4

%I #6 Jul 23 2023 13:42:31

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

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

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

%N Number of divisors of n of the form 5*k+1 that are at most sqrt(n).

%F G.f.: Sum_{k>=0} x^(5*k+1)^2 / (1 - x^(5*k+1)).

%t Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{1}, Mod[#, 5]] &)], {n, 100}]

%t nmax = 100; CoefficientList[Series[Sum[x^(5 k + 1)^2/(1 - x^(5 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

%Y Cf. A001876, A038548, A364389.

%K nonn

%O 1,36

%A _Ilya Gutkovskiy_, Jul 21 2023