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Number of divisors of n of the form 5*k+2 that are at most sqrt(n).
3

%I #5 Jul 23 2023 13:42:22

%S 0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,

%T 0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,2,0,1,0,1,0,1,1,1,0,1,0,1,

%U 0,2,0,1,0,1,0,1,1,1,0,1,0,1,0,2,0,1,0,1,0,1,1,1,0,1,0,1,0,2,0,1

%N Number of divisors of n of the form 5*k+2 that are at most sqrt(n).

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

%t Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{2}, Mod[#, 5]] &)], {n, 100}]

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

%Y Cf. A001877, A038548, A364388.

%K nonn

%O 1,56

%A _Ilya Gutkovskiy_, Jul 21 2023