A243995 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.

1, 18, 96, 560, 720, 1056, 1760, 2000, 3264, 7392, 30960, 50800, 172080, 173440, 9561600, 13304064, 195522560, 1017856448, 1026021024, 1568010240, 2817884160

Offset: 1

Author

Paolo P. Lava, Jun 18 2014

Keywords

• nonn
• more

Comments

a(22) > 10^10. - Amiram Eldar, Jan 27 2019

Examples

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

Crossrefs

Cf. A000005, A000010, A000203, A077092.

Programs

Maple

with(numtheory): P:=proc(q) local n;
for n from 1 to q do
if phi(sigma(n)-phi(n)-tau(n))=n then print(n);
fi; od; end: P(10^10);

Mathematica

Select[Range[10^4], EulerPhi[DivisorSigma[1, #] - EulerPhi[#] - DivisorSigma[0, #]] == # &] (* Alonso del Arte, Jun 18 2014 *)

PARI

isok(n) = (spd = sigma(n) - eulerphi(n) - numdiv(n)) && (eulerphi(spd) == n); \\ Michel Marcus, Jun 18 2014

Extensions

a(15)-a(16) from Jens Kruse Andersen, Jul 23 2014

a(17)-a(21) from Amiram Eldar, Jan 27 2019