cp's OEIS Frontend

A230373 Numbers n such that sigma(sigma*(n)) = sigma*(sigma(n)), where sigma*(n) is the sum of anti-divisors of n (A066417).

%I A230373 #17 Oct 19 2014 15:57:52
%S A230373 3,265,450,1989,18278,31639,55474,71306,96639,197518,267026,1620723,
%T A230373 1888235,3605481,4448715,10837215,12128451,22598820,84681074,96503379,
%U A230373 130118331,152234714,162138375,189149834,211239421,343379954,353833749,404994939,599244123,804486314
%N A230373 Numbers n such that sigma(sigma*(n)) = sigma*(sigma(n)), where sigma*(n) is the sum of anti-divisors of n (A066417).
%e A230373 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 A230373 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 A230373 Therefore 450 is part of the sequence because sigma(sigma*(450)) = sigma*(sigma(450)) = 1266.
%p A230373 with(numtheory);P:=proc(q) local a,b,c,k,j,n;
%p A230373 for n from 3 to q do c:=sigma(n);
%p A230373 k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A230373 a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2;
%p A230373 k:=0; j:=c; while j mod 2<>1 do k:=k+1; j:=j/2; od;
%p A230373 b:=sigma(2*c+1)+sigma(2*c-1)+sigma(c/2^k)*2^(k+1)-6*c-2;
%p A230373 if sigma(a)=b then print(n); fi; od; end: P(10^6);
%Y A230373 Cf. A000203, A066417.
%K A230373 nonn,hard
%O A230373 1,1
%A A230373 _Paolo P. Lava_, Oct 23 2013
%E A230373 a(12)-a(30) from _Giovanni Resta_, Oct 23 2013