A333752 Sum of squarefree divisors of n that are <= sqrt(n).

1, 1, 1, 3, 1, 3, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 1, 3, 4, 3, 1, 6, 6, 3, 4, 3, 1, 11, 1, 3, 4, 3, 6, 12, 1, 3, 4, 8, 1, 12, 1, 3, 9, 3, 1, 12, 8, 8, 4, 3, 1, 12, 6, 10, 4, 3, 1, 17, 1, 3, 11, 3, 6, 12, 1, 3, 4, 15, 1, 12, 1, 3, 9, 3, 8, 12, 1, 8, 4, 3, 1, 19, 6, 3, 4, 3, 1, 17

Offset

1,4

Links

Table of n, a(n) for n=1..90.

Formula

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

Mathematica

Table[DivisorSum[n, # &, # <= Sqrt[n] && SquareFreeQ[#] &], {n, 1, 90}]
nmax = 90; CoefficientList[Series[Sum[MoebiusMu[k]^2 k x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

Prog

(PARI) a(n) = sumdiv(n, d, if ((d^2<=n) && issquarefree(d), d)); \\ Michel Marcus, Apr 03 2020

Crossrefs

Cf. A005117, A048250, A066839, A069289, A069293, A097974, A333749, A333751, A333753.

Sequence in context: A110919 A281273 A109599 * A066839 A176246 A046933

Adjacent sequences: A333749 A333750 A333751 * A333753 A333754 A333755

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2020

Status

approved