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%I #22 Jan 28 2019 13:59:08
%S 8,104,512,1488,9680,73728,603680,2508800,1085407232,29473106432
%N Numbers n such that sigma(2*n-1) = 3*n, where sigma(k) is the sum of the positive divisors of k.
%C 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 It is conjectured that all terms of this sequence are even numbers.
%C a(11) > 5*10^11, according to _Giovanni Resta_ at A063906. - _Amiram Eldar_, Jan 27 2019
%F a(n) = (A063906(n)+1)/2. - _Amiram Eldar_, Jan 27 2019
%e Example: a(1)=8 since sigma(15)= 24 = 3*8.
%t Select[Range[10^5], DivisorSigma[1, 2# - 1] == 3# &] (* _Alonso del Arte_, May 19 2011 *)
%o (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,print(c););c1 = c1 +2;c2 = c2 +3;c = c+1);}
%Y Cf. A000203, A000396, A063906.
%K nonn,more
%O 1,1
%A _Luis H. Gallardo_, May 19 2011
%E a(9)-a(10) added from the data at A063906 by _Amiram Eldar_, Jan 27 2019
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