%I #12 Oct 08 2013 09:12:26
%S 154,3136,5536,20066,136036,9550080,78011830
%N Numbers n for which n = sigma*(x) = sigma*(y), where n = x + y and sigma*(n) is the sum of the anti-divisors of n.
%C Up to a(7) the triples (n, x, y) are (154, 77, 77), (3136, 1568, 1568)(5536, 2768, 2768), (20066, 10368, 9698), (136036, 80753, 55283), (9550080, 4775040, 4775040), (78011830, 39348342, 38663488). - _Giovanni Resta_, Oct 08 2013
%e n = 20066 = 9698 + 10368.
%e Anti-divisors of 9698 are 3, 4, 5, 7, 9, 15, 17, 45, 52, 119, 163, 431, 1141, 1293, 1492, 2155, 2771, 3879, 6465 and their sum is 20066 that is equal to n.
%e Anti-divisors of 10368 are 5, 11, 13, 29, 55, 65, 89, 143, 145, 233, 256, 319, 377, 715, 768, 1595, 1885, 2304, 4147, 6912 and their sum is 20066 that is equal to n.
%p with(numtheory); P:=proc(q) local a,b, i, j, k, n;
%p for n from 1 to q do for i from 1 to trunc(n/2) do
%p k:=0; j:=i; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p a:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
%p k:=0; j:=n-i; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p b:=sigma(2*(n-i)+1)+sigma(2*(n-i)-1)+sigma((n-i)/2^k)*2^(k+1)-6*(n-i)-2;
%p if a=b and a=n then print(n); fi; od; od; end: P(10^6);
%Y Cf. A066272, A066417, A210732.
%K nonn
%O 1,1
%A _Paolo P. Lava_, Oct 07 2013
%E a(5)-a(7) from _Giovanni Resta_, Oct 08 2013