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 A386589 #3 Jul 26 2025 12:40:22
%S A386589 1,3,4,4,2,12,2,5,5,5,2,25,2,18,20,6,2,14,2,7,6,5,2,27,3,5,6,20,2,59,
%T A386589 2,7,6,5,38,28,2,5,6,9,2,70,2,7,22,5,2,29,3,7,6,7,2,16,4,77,6,5,2,74,
%U A386589 2,5,8,8,4,16,2,7,6,125,2,31,2,5,22,7,4,93,2,11,7,5,2,85,4,5,6,9,2,63,4,7,6,5,4,31,2,20,8,10
%N A386589 a(n) = Sum_{d|n} d^c(d), where c = A351114.
%C A386589 Inverse Möbius transform of n^c(n), where c = A351114.
%C A386589 For each divisor d of n, add d if d is a balanced number (A020492), else add 1.
%F A386589 a(n) = Sum_{d|n} 1 + (d - 1)*c(d), where c = A351114.
%F A386589 a(n) = A000005(n) + A351113(n) - A351112(n).
%t A386589 Table[Sum[d^(1 - Ceiling[DivisorSigma[1, d]/EulerPhi[d]] + Floor[DivisorSigma[1, d]/EulerPhi[d]]), {d, Divisors[n]}], {n, 100}]
%Y A386589 Cf. A000005 (tau), A020492 (balanced numbers), A351112, A351113, A351114.
%K A386589 nonn
%O A386589 1,2
%A A386589 _Wesley Ivan Hurt_, Jul 26 2025