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 A084306 #13 Nov 19 2017 01:41:27
%S A084306 121,304,127744,33501184,8589082624
%N A084306 Numbers x such that sigma(x) mod x = 12 and x is not divisible by 6. Singular solutions mentioned in A076496.
%C A084306 If n = P*q, where P is a multiple perfect number and q is prime so that gcd(P,q) = 1, then sigma(n) = kn(q+1). Consequently sigma(n) = knq + kn sigma(n) mod n = kn. Such values of n are regular solutions to this and analogous cases. Here, not these but the additional eccentric solutions are collected. Cf. A076496.
%C A084306 a(6) > 10^11. - _Donovan Johnson_, Sep 20 2012
%C A084306 If p = 2^k - 13 > 3 is a prime number, then 2^(k-1)*p is a term. This happens for k = 5, 9, 13, 17, 57, 105, 137, 3217, ... (A096818). - _Giovanni Resta_, Apr 01 2014
%e A084306 n = 33501184 = 4096*8179; sigma(n) = 2n + 12 = 67002380.
%t A084306 Do[s=Mod[DivisorSigma[1, n], n]; If[IntegerQ[n/100000], Print[{n}]]; If[Equal[s, 12]&&!Equal[Mod[n, 6], 0], Print[n]], {n, 1, 100000000}]
%Y A084306 Cf. A076496, A076495, A000396, A045768-A045770, A007691, A096818.
%K A084306 nonn
%O A084306 1,1
%A A084306 _Labos Elemer_, Jun 11 2003
%E A084306 a(5) from _Donovan Johnson_, Sep 20 2012