A364357 Number of divisors of n of the form 3*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, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 0, 3, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2

Offset: 1

Author

Ilya Gutkovskiy, Jul 21 2023

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001822, A038548, A364209.

Programs

Maple

N:= 100: # for a(1) .. a(N)
M:= floor((sqrt(N)-3)/2):
G:= series(add(x^((3*k+2)^2)/(1-x^(3*k+2)),k=0..M),x,N+1):
seq(coeff(G,x,i),i=1..N); # Robert Israel, Jun 05 2024

Mathematica

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

Formula

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