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 A190786 #33 Aug 02 2025 09:57:14
%S A190786 8,104,512,1488,9680,73728,603680,2508800,1085407232,29473106432,
%T A190786 583166845500512,18236498181611824400
%N A190786 Numbers m such that sigma(2*m-1) = 3*m, where sigma(k) is the sum of the positive divisors of k.
%C A190786 All even perfect numbers are of the form z(2*z-1) with z = 2^(p-1), p prime and 2*z-1 = 2^p-1 prime. It is unknown if there are any odd perfect numbers of this same form. The equation defining the sequence appears while working a special case of the conjecture.
%C A190786 It is conjectured that all terms of this sequence are even numbers.
%F A190786 a(n) = (A063906(n)+1)/2. - _Amiram Eldar_, Jan 27 2019
%e A190786 a(1)=8 is a term since sigma(15) = 24 = 3*8.
%t A190786 Select[Range[10^5], DivisorSigma[1, 2# - 1] == 3# &] (* _Alonso del Arte_, May 19 2011 *)
%o A190786 (PARI) zt(a,b) = {local(c,c1,c2,s); c =a ; c1 = 2*c-1;c2 = 3*c;while(c<b, s = sigma(c1);if(s == c2,print1(c, ", "););c1 = c1 +2;c2 = c2 +3;c = c+1);}
%Y A190786 Cf. A000203, A000396, A063906.
%K A190786 nonn,more
%O A190786 1,1
%A A190786 _Luis H. Gallardo_, May 19 2011
%E A190786 a(9)-a(10) added from the data at A063906 by _Amiram Eldar_, Jan 27 2019
%E A190786 a(11) from _Max Alekseyev_, May 22 2025
%E A190786 a(12) from _Max Alekseyev_, Jul 30 2025