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A227977 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.

%I A227977 #12 Oct 08 2013 09:12:26
%S A227977 154,3136,5536,20066,136036,9550080,78011830
%N A227977 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 A227977 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 A227977 n = 20066 = 9698 + 10368.
%e A227977 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 A227977 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 A227977 with(numtheory); P:=proc(q) local a,b, i, j, k, n;
%p A227977 for n from 1 to q do for i from 1 to trunc(n/2) do
%p A227977 k:=0; j:=i; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A227977 a:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
%p A227977 k:=0; j:=n-i; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A227977 b:=sigma(2*(n-i)+1)+sigma(2*(n-i)-1)+sigma((n-i)/2^k)*2^(k+1)-6*(n-i)-2;
%p A227977 if a=b and a=n then print(n); fi; od; od; end: P(10^6);
%Y A227977 Cf. A066272, A066417, A210732.
%K A227977 nonn
%O A227977 1,1
%A A227977 _Paolo P. Lava_, Oct 07 2013
%E A227977 a(5)-a(7) from _Giovanni Resta_, Oct 08 2013