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 A335289 #12 May 31 2020 02:12:34
%S A335289 1492260,1741740,2369640,7192260,83445180,91798980,104370420,
%T A335289 125214180,141996120,148532076,162910980,171175788,196899780,
%U A335289 199793412,201246660,229849620,297085860,298993140,398023080,442859940,540201480,548305740,796792920,801375660,835975140
%N A335289 Nonsquarefree numbers that are both balanced numbers (A020492) and unitary balanced numbers (A335288).
%C A335289 The squarefree balanced numbers (A078557) are also unitary balanced numbers (A335288), since all the divisors of squarefree numbers are unitary, and thus if k is squarefree, then sigma(k) = usigma(k) and phi(k) = uphi(k).
%H A335289 Amiram Eldar, <a href="/A335289/b335289.txt">Table of n, a(n) for n = 1..4045</a> (calculated using data from _Jud McCranie_)
%e A335289 1492260 is a term since sigma(1492260)/phi(1492260) = 5806080/276480 = 21 is an integer, usigma(1492260)/uphi(1492260) = 4147200/414720 = 10 is an integer, and 1492260 is not squarefree since it is divisible by 4 = 2^2.
%t A335289 f1[1, 1] = 1; f1[p_, e_] := (p^(e+1) - 1)/p^(e-1)/(p-1)^2; f2[1, 1] = 1; f2[p_, e_] := (p^e + 1)/(p^e -1); balQ[n_] := And @@ IntegerQ /@ Times@@({f1[#1, #2], f2[#1, #2]}& @@@ FactorInteger[n]); Select[Range[3*10^6], !SquareFreeQ[#] && balQ[#] &]
%Y A335289 Intersection of A013929, A020492 and A335288.
%Y A335289 Cf. A000010 (phi), A000203 (sigma), A047994 (uphi), A034448 (usigma), A078557.
%K A335289 nonn
%O A335289 1,1
%A A335289 _Amiram Eldar_, May 30 2020