This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A386573 #9 Jul 26 2025 22:48:25
%S A386573 1,3,4,3,1,12,1,3,4,3,1,12,1,17,19,3,1,12,1,3,4,3,1,12,1,3,4,17,1,57,
%T A386573 1,3,4,3,36,12,1,3,4,3,1,68,1,3,19,3,1,12,1,3,4,3,1,12,1,17,4,3,1,57,
%U A386573 1,3,4,3,1,12,1,3,4,122,1,12,1,3,19,3,1,90,1,3,4,3,1,68,1,3,4,3,1,57,1,3,4,3,1,12,1,17,4,3
%N A386573 Sum of the squarefree balanced divisors of n.
%C A386573 Inverse Möbius transform of n * c(n) * mu(n)^2, where c = A351114.
%F A386573 a(n) = Sum_{d|n} d * c(d) * mu(d)^2, where c = A351114.
%t A386573 Table[Sum[d (1 - Ceiling[DivisorSigma[1, d]/EulerPhi[d]] + Floor[DivisorSigma[1, d]/EulerPhi[d]]) MoebiusMu[d]^2, {d, Divisors[n]}], {n, 100}]
%Y A386573 Cf. A005117 (squarefree numbers), A020492 (balanced numbers), A078557, A351114, A386574.
%K A386573 nonn
%O A386573 1,2
%A A386573 _Wesley Ivan Hurt_, Jul 26 2025