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

1,2

Comments

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

Links

Table of n, a(n) for n=1..21.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000005, A000010, A000203, A077092.

Sequence in context: A275253 A034725 A047929 * A264202 A338783 A324304

Adjacent sequences: A243992 A243993 A243994 * A243996 A243997 A243998

Keyword

nonn,more

Author

Paolo P. Lava, 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

Status

approved