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.
a(6) = 8 is a term because A340179(8) = 4 = 2^2.
f:= proc(n) local C, s, c; C:=select(t -> igcd(t, n) = 1, [$1..n-1]); s:= convert(C, `+`); add(s mod c, c = C) end proc: select(t -> issqr(f(t)), [$1..7000]);
a(4) = 16 is a term because A340179(16) = 32 = 2*16.
f:= proc(n) local C, s, c; C:=select(t -> igcd(t, n) = 1, [$1..n-1]); s:= convert(C, `+`); add(s mod c, c = C) end proc: select(t -> f(t) mod t = 0, [$1..5000]);
A340179[n_] := Total@Mod[#2, #1]& @@ {#, Total@#}& @ Select[Range[n], GCD[#, n] == 1&]; Reap[For[k = 1, k <= 80000, k++, If[Divisible[A340179[k], k], Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, May 16 2023, after Michael De Vlieger in A340179 *)