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

1,56

Links

Table of n, a(n) for n=1..100.

Formula

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

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

Crossrefs

Cf. A001877, A038548, A364388.

Sequence in context: A083889 A360079 A127523 * A116927 A137276 A287234

Adjacent sequences: A364386 A364387 A364388 * A364390 A364391 A364392

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2023

Status

approved