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A210732 Numbers n for which sigma*(n)=sigma*(x)+sigma*(y), where n=x+y and sigma*(n) is the sum of the anti-divisors of n.

%I A210732 #8 May 16 2012 11:58:13
%S A210732 6,9,15,18,21,24,27,30,31,33,37,39,43,44,46,47,53,56,57,62,65,66,70,
%T A210732 73,74,75,76,78,81,83,86,88,90,91,92,93,97,99,102,103,106,107,109,110,
%U A210732 114,116,117,118,119,121,122,123,125,126,127,129,131,133,135,136
%N A210732 Numbers n for which sigma*(n)=sigma*(x)+sigma*(y), where n=x+y and sigma*(n) is the sum of the anti-divisors of n.
%C A210732 Similar to A211223 but using anti-divisors.
%e A210732 sigma*(127)=sigma*(45)+sigma*(82) that is 212=86+126.
%e A210732 In more than one way:
%e A210732 sigma*(133)=sigma*(50)+sigma*(83)=sigma*(52)+sigma*(81) that is
%e A210732 204=80+124=94+110.
%p A210732 with(numtheory);
%p A210732 A210732:=proc(q)
%p A210732 local a,b,c,i,j,k,n;
%p A210732 for n from 3 to q do
%p A210732   a:=0;
%p A210732   for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; fi; od;
%p A210732   for i from 1 to trunc(n/2) do
%p A210732    b:=0; c:=0;
%p A210732    for k from 2 to i-1 do if abs((i mod k)-k/2)<1 then b:=b+k; fi; od;
%p A210732    for k from 2 to n-i-1 do if abs(((n-i) mod k)-k/2)<1 then c:=c+k; fi; od;
%p A210732    if a=b+c then print(n); break; fi;
%p A210732   od;
%p A210732 od; end:
%p A210732 A210732(10000);
%Y A210732 Cf. A066272, A066417, A083207, A204830, A204831, A211223-A211225.
%K A210732 nonn
%O A210732 3,1
%A A210732 _Paolo P. Lava_, May 10 2012