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%I #23 Sep 28 2015 03:31:46
%S 7,10,14,16,45,86,2379,2324,4213,5866,27323,33604,1303227,1737628,
%T 3722831,4208308,15752651,18706108,6094085371,8114352508,30090695519,
%U 40119052564
%N Pairs of numbers a, b for which sigma*(a)=b and sigma(b)-b-1=a, where sigma*(n) is the sum of the anti-divisors of n.
%C Betrothed numbers mixed with anti-divisors.
%C a(23) > 10^11. - _Hiroaki Yamanouchi_, Sep 28 2015
%e sigma*(45)= 2+6+7+10+13+18+30 = 86.
%e sigma(86)-86-1 = 2+43 = 45.
%e sigma*(2379) = 2+6+26+67+71+78+122+366+1586 = 2374.
%e sigma(2324)-2324-1 = 2+4+7+14+28+83+166+332+581+1162 = 2379.
%p with(numtheory); P:= proc(n) local b,c,i,j,k;
%p for i from 3 to n do k:=0; j:=i;
%p while j mod 2 <> 1 do k:=k+1; j:=j/2; od;
%p b:=sigma(2*i+1)+sigma(2*i-1)+sigma(i/2^k)*2^(k+1)-6*i-2;
%p if sigma(b)-b-1=i then print(i); print(b); fi;
%p od; end: P(10^9);
%Y Cf. A005276, A066272, A192290, A192291, A192293.
%K nonn,more,tabf
%O 1,1
%A _Paolo P. Lava_, Jun 29 2011
%E a(13)-a(14) from _Paolo P. Lava_, Dec 03 2014
%E a(7)-a(8) swapped and a(15)-a(22) added by _Hiroaki Yamanouchi_, Sep 28 2015
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