A363277 Sum of the divisor complements of the squarefree divisors of n that are <= sqrt(n).

1, 2, 3, 6, 5, 9, 7, 12, 12, 15, 11, 22, 13, 21, 20, 24, 17, 33, 19, 30, 28, 33, 23, 44, 30, 39, 36, 42, 29, 61, 31, 48, 44, 51, 42, 72, 37, 57, 52, 68, 41, 84, 43, 66, 69, 69, 47, 96, 56, 85, 68, 78, 53, 108, 66, 92, 76, 87, 59, 132, 61, 93, 93, 96, 78, 132, 67, 102, 92

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Formula

a(n) = n * Sum_{d|n, d<=sqrt(n)} mu(d)^2 / d.

Example

a(16) = 16 * Sum_{d|16, d<=sqrt(16)} mu(d)^2 / d = 16 * (mu(1)^2/1 + mu(2)^2/2) = 16 * (1 + 1/2) = 24.

Mathematica

a[n_] := DivisorSum[n, n/# &, #^2 <= n && SquareFreeQ[#] &]; Array[a, 100] (* Amiram Eldar, May 25 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, if (issquarefree(d) && (d^2 <= n), n/d)); \\ Michel Marcus, May 25 2023

Crossrefs

Cf. A070038, A333749.

Sequence in context: A257011 A144652 A035493 * A070038 A328638 A327420

Adjacent sequences: A363274 A363275 A363276 * A363278 A363279 A363280

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 25 2023

Status

approved