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

Author

Ilya Gutkovskiy, Jul 21 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A001826, A038548, A364387.

Programs

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

Formula

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