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 A110590 #22 Jun 17 2025 10:06:03
%S A110590 1,2,3,6,12,14,15,30,264,3828
%N A110590 Balanced numbers k (A020492) such that phi(k) is not divisible by 12.
%C A110590 The only balanced numbers k such that sigma(k) is not divisible by 12 are 1, 2, 3.
%C A110590 a(11) if it exists is greater than 10^8. - _Michel Marcus_, Aug 06 2013
%C A110590 a(11) if it exists is greater than 10^13. - _Giovanni Resta_, Jul 13 2015
%C A110590 a(11) if it exists is greater than 6.5*10^14 (checked using data from _Jud McCranie_). - _Amiram Eldar_, Nov 10 2024
%F A110590 k such that sigma(k)/phi(k) is an integer and phi(k) mod 12 != 0.
%p A110590 with(numtheory): BNM:=[]: for z from 1 to 1 do for n from 1 to 100000 do if phi(n) mod 12 > 0 and sigma(n) mod phi(n) = 0 then BNM:=[op(BNM),n] fi; od; od; BNM; # after 3828 there are no others up to 2*10^6.
%t A110590 fQ[n_] := Block[{ds = DivisorSigma[1, n], ep = EulerPhi@n}, Mod[ep, 12] > 0 && IntegerQ[ds/ep]]; Do[ If[ fQ@n, Print@n], {n, 4*10^8}] (* _Robert G. Wilson v_, Jun 19 2006 *)
%Y A110590 Cf. A000010, A000203, A020492.
%K A110590 nonn,more
%O A110590 1,2
%A A110590 _Walter Kehowski_, Sep 13 2005