A364358 Number of divisors of n of the form 4*k+1 that are at most sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2

Offset

1,25

Links

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

Formula

G.f.: Sum_{k>=0} x^(4*k+1)^2 / (1 - x^(4*k+1)).

Maple

f:= proc(n) nops(select(t -> t mod 4 = 1 and t^2 <= n, numtheory:-divisors(n))) end proc:
map(f, [$1..100]); # Robert Israel, Dec 29 2024

Mathematica

Table[Count[Divisors[n], _?(# <= Sqrt[n] && MemberQ[{1}, Mod[#, 4]] &)], {n, 100}]
nmax = 100; CoefficientList[Series[Sum[x^(4 k + 1)^2/(1 - x^(4 k + 1)), {k, 0, nmax}], {x, 0, nmax}], x] // Rest

Crossrefs

Cf. A001826, A038548, A364387.

Sequence in context: A140345 A177706 A130782 * A055457 A277873 A032542

Adjacent sequences: A364355 A364356 A364357 * A364359 A364360 A364361

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2023

Status

approved