A243995 - OEIS

%I #18 Jan 27 2019 05:45:50

%S 1,18,96,560,720,1056,1760,2000,3264,7392,30960,50800,172080,173440,

%T 9561600,13304064,195522560,1017856448,1026021024,1568010240,

%U 2817884160

%N Fixed points of the function a(n) = phi(sigma(n) - phi(n) - d(n)), where phi(n) is the Euler totient function, sigma(n) the sum of divisors of n and d(n) the number of divisors of n.

%C a(22) > 10^10. - _Amiram Eldar_, Jan 27 2019

%e sigma(96) = 252, phi(96) = 32, d(96) = 12 and phi(252 - 32 - 12) = 96.

%p with(numtheory): P:=proc(q) local n;

%p for n from 1 to q do

%p if phi(sigma(n)-phi(n)-tau(n))=n then print(n);

%p fi; od; end: P(10^10);

%t Select[Range[10^4], EulerPhi[DivisorSigma[1, #] - EulerPhi[#] - DivisorSigma[0, #]] == # &] (* _Alonso del Arte_, Jun 18 2014 *)

%o (PARI) isok(n) = (spd = sigma(n) - eulerphi(n) - numdiv(n)) && (eulerphi(spd) == n); \\ _Michel Marcus_, Jun 18 2014

%Y Cf. A000005, A000010, A000203, A077092.

%K nonn,more

%O 1,2

%A _Paolo P. Lava_, Jun 18 2014

%E a(15)-a(16) from _Jens Kruse Andersen_, Jul 23 2014

%E a(17)-a(21) from _Amiram Eldar_, Jan 27 2019