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

Author

Wesley Ivan Hurt, May 26 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A092261.

Programs

Mathematica

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

PARI

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

Formula

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