A363289 Sum of the divisor complements of the unitary squarefree divisors of n.

1, 3, 4, 4, 6, 12, 8, 8, 9, 18, 12, 16, 14, 24, 24, 16, 18, 27, 20, 24, 32, 36, 24, 32, 25, 42, 27, 32, 30, 72, 32, 32, 48, 54, 48, 36, 38, 60, 56, 48, 42, 96, 44, 48, 54, 72, 48, 64, 49, 75, 72, 56, 54, 81, 72, 64, 80, 90, 60, 96, 62, 96, 72, 64, 84, 144, 68, 72, 96, 144, 72

Offset

1,2

Links

Table of n, a(n) for n=1..71.

Formula

a(n) = n * Sum_{d|n, gcd(d,n/d)=1} mu(d)^2 / d.

Mathematica

a[n_] := DivisorSum[n, n/# &, CoprimeQ[#, n/#] && SquareFreeQ[#] &]; Array[a, 100] (* Amiram Eldar, May 26 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, if ((gcd(d, n/d) == 1) && issquarefree(d), n/d)); \\ Michel Marcus, May 26 2023

Crossrefs

Cf. A092261.

Sequence in context: A178450 A378435 A325973 * A019462 A078071 A359789

Adjacent sequences: A363286 A363287 A363288 * A363290 A363291 A363292

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 26 2023

Status

approved