A364209 Number of divisors of n of the form 3*k+1 that are at most sqrt(n).

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, 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, 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

Offset

1,16

Links

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

Formula

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

Mathematica

Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{1}, Mod[#, 3]] &)], {n, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(3 k + 1)^2/(1 - x^(3 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A001817, A038548, A364357.

Sequence in context: A177704 A138191 A069291 * A268238 A081117 A368334

Adjacent sequences: A364206 A364207 A364208 * A364210 A364211 A364212

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2023

Status

approved