A364389 Number of divisors of n of the form 5*k+2 that are at most sqrt(n).

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, 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, 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

Offset: 1

Author

Ilya Gutkovskiy, Jul 21 2023

Keywords

• nonn

Crossrefs

Cf. A001877, A038548, A364388.

Programs

Mathematica

Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{2}, Mod[#, 5]] &)], {n, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(5 k + 2)^2/(1 - x^(5 k + 2)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

Formula

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