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%I #17 Oct 19 2014 15:57:52
%S 3,265,450,1989,18278,31639,55474,71306,96639,197518,267026,1620723,
%T 1888235,3605481,4448715,10837215,12128451,22598820,84681074,96503379,
%U 130118331,152234714,162138375,189149834,211239421,343379954,353833749,404994939,599244123,804486314
%N Numbers n such that sigma(sigma*(n)) = sigma*(sigma(n)), where sigma*(n) is the sum of anti-divisors of n (A066417).
%e Divisors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450 and sigma(450) = 1209; anti-divisors of 1209 are 2, 6, 26, 41, 59, 62, 78, 186, 806 and sigma*(1209) = 1266.
%e Anti-divisors of 450 are 4, 12, 17, 20, 29, 31, 36, 53, 60, 100, 180, 300 and sigma*(450) = 842; divisors of 842 are 1, 2, 421, 842 and sigma(842) = 1266.
%e Therefore 450 is part of the sequence because sigma(sigma*(450)) = sigma*(sigma(450)) = 1266.
%p with(numtheory);P:=proc(q) local a,b,c,k,j,n;
%p for n from 3 to q do c:=sigma(n);
%p k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p k:=0; j:=c; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p b:=sigma(2*c+1)+sigma(2*c-1)+sigma(c/2^k)*2^(k+1)-6*c-2;
%p if sigma(a)=b then print(n); fi; od; end: P(10^6);
%Y Cf. A000203, A066417.
%K nonn,hard
%O 1,1
%A _Paolo P. Lava_, Oct 23 2013
%E a(12)-a(30) from _Giovanni Resta_, Oct 23 2013
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