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 A386592 #10 Aug 26 2025 17:57:18
%S A386592 0,0,0,4,5,0,7,12,9,15,11,4,13,7,5,28,17,27,19,39,28,33,23,36,30,39,
%T A386592 36,39,29,15,31,60,44,51,12,67,37,57,52,87,41,28,43,81,59,69,47,100,
%U A386592 56,90,68,95,53,108,71,47,76,87,59,99,61,93,100,124,83,132,67,123,92,22,71,171,73,111,105,137,95,78,79,183,117,123,83,144,107,129,116,177
%N A386592 Sum of the divisors of n that are not balanced numbers.
%C A386592 Sum of the divisors d of n such that phi(d) does not divide sigma(d).
%C A386592 Inverse Möbius transform of n * (1 - c(n)), where c = A351114.
%H A386592 Robert Israel, <a href="/A386592/b386592.txt">Table of n, a(n) for n = 1..10000</a>
%F A386592 a(n) = Sum_{d|n} d * (1 - c(d)), where c = A351114.
%F A386592 a(n) = A000203(n) - A351113(n).
%p A386592 g:= proc(n) option remember; numtheory:-sigma(n) mod numtheory:-phi(n) <> 0 end proc:
%p A386592 f:= n -> convert(select(g,numtheory:-divisors(n)),`+`):
%p A386592 map(f, [$1..100]); # _Robert Israel_, Aug 26 2025
%t A386592 Table[Sum[d (Ceiling[DivisorSigma[1, d]/EulerPhi[d]] - Floor[DivisorSigma[1, d]/EulerPhi[d]]), {d, Divisors[n]}], {n, 100}]
%Y A386592 Cf. A000010 (phi), A000203 (sigma), A351113, A351114, A387333.
%K A386592 nonn,look,changed
%O A386592 1,4
%A A386592 _Wesley Ivan Hurt_, Jul 26 2025