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Numbers n such that sigma(phi(n)) - phi(n) = n + phi(sigma(n)-n); that is, f(g(n)) - g(f(n)) = n where f = A001065 and g = A000010.
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%I #14 Sep 05 2017 11:54:20

%S 52298,88694,13868696,18816288938

%N Numbers n such that sigma(phi(n)) - phi(n) = n + phi(sigma(n)-n); that is, f(g(n)) - g(f(n)) = n where f = A001065 and g = A000010.

%C a(5) > 45*10^9. - _Giovanni Resta_, Sep 05 2017

%e 52298 is a term because phi(sigma(52298) - 52298) = phi(27382) = 13690, sigma(phi(52298)) - phi(52298) = sigma(25740) - 25740 = 65988 and 65988 - 13690 = 52298.

%o (PARI) a001615(n) = sigma(n)-n;

%o isok(n) = a001615(eulerphi(n))==n+eulerphi(a001615(n));

%Y Cf. A000010, A001065, A062401, A062402.

%K nonn,more

%O 1,1

%A _Altug Alkan_, Sep 04 2017

%E a(4) from _Giovanni Resta_, Sep 05 2017