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

1,30

Links

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

Formula

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

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

Crossrefs

Cf. A001822, A038548, A364209.

Sequence in context: A246690 A317748 A090465 * A052344 A339375 A147768

Adjacent sequences: A364354 A364355 A364356 * A364358 A364359 A364360

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2023

Status

approved