A363318 Total distance from n to each of its refactorable unitary divisors.

0, 1, 2, 3, 4, 9, 6, 7, 8, 17, 10, 11, 12, 25, 14, 15, 16, 42, 18, 19, 20, 41, 22, 39, 24, 49, 26, 27, 28, 57, 30, 31, 32, 65, 34, 62, 36, 73, 38, 71, 40, 81, 42, 43, 80, 89, 46, 47, 48, 97, 50, 51, 52, 105, 54, 103, 56, 113, 58, 107, 60, 121, 116, 63, 64, 129, 66, 67, 68, 137, 70

Offset: 1

Author

Wesley Ivan Hurt, May 27 2023

Keywords

• nonn
• easy

Crossrefs

Cf. A363085, A363298.

Programs

Mathematica

a[n_] := DivisorSum[n, n - # &, CoprimeQ[#, n/#] && Divisible[#, DivisorSigma[0, #]] &]; Array[a, 100]

Formula

a(n) = Sum_{d|n, tau(d)|d, gcd(d,n/d)=1} (n - d).

a(n) = n * A363298(n) - A363085(n).