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 A386591 #15 Aug 26 2025 15:13:48
%S A386591 0,0,0,1,1,0,1,2,1,2,1,1,1,1,1,3,1,2,1,4,2,2,1,3,2,2,2,3,1,2,1,4,2,2,
%T A386591 2,4,1,2,2,6,1,2,1,4,3,2,1,5,2,4,2,4,1,4,3,4,2,2,1,5,1,2,4,5,3,4,1,4,
%U A386591 2,3,1,7,1,2,3,4,3,3,1,8,3,2,1,5,3,2,2,6,1,6,3,4,2,2,3,7,1,3,4,7
%N A386591 Number of divisors of n that are not balanced numbers.
%C A386591 Number of divisors d of n such that phi(d) does not divide sigma(d).
%C A386591 Inverse Möbius transform of 1 - c(n), where c = A351114.
%H A386591 Robert Israel, <a href="/A386591/b386591.txt">Table of n, a(n) for n = 1..10000</a>
%F A386591 a(n) = Sum_{d|n} (1 - c(d)), where c = A351114.
%F A386591 a(n) = A000005(n) - A351112(n).
%p A386591 g:= proc(n) option remember; numtheory:-sigma(n) mod numtheory:-phi(n) <> 0 end proc:
%p A386591 f:= n -> nops(select(g,numtheory:-divisors(n))):
%p A386591 map(f, [$1..100]); # _Robert Israel_, Aug 26 2025
%t A386591 Table[Sum[Ceiling[DivisorSigma[1, d]/EulerPhi[d]] - Floor[DivisorSigma[1, d]/EulerPhi[d]], {d, Divisors[n]}], {n, 100}]
%o A386591 (PARI) a(n) = sumdiv(n, d, sigma(d)%eulerphi(d) != 0); \\ _Michel Marcus_, Aug 26 2025
%Y A386591 Cf. A000005 (tau), A000010 (phi), A000203 (sigma), A020492 (balanced numbers), A351112, A351114.
%K A386591 nonn,changed
%O A386591 1,8
%A A386591 _Wesley Ivan Hurt_, Jul 26 2025