A238229 Numbers n such that if x = sigma(n)-phi(n)+tau(n)-n then n = sigma(x)-phi(x)+tau(x)-x.

2, 4, 20, 66, 342, 34092, 40842, 41922, 46242, 55422, 207624, 259448, 533172, 547300, 571992, 667408, 1531032, 1786288, 10983114, 114013752, 133506680, 323277822, 347360860, 386144360, 387415458, 459603716, 476991704, 1443279992, 1539484232, 15537978552

Offset

1,1

Comments

The fixed points (terms with x = n) are 2, 4, 20, 66, 342, 41922, 10983114, ... - Amiram Eldar, Mar 31 2019

Links

Kevin P. Thompson, Table of n, a(n) for n = 1..38

Example

Fixed points: 2, 4, 20, 66, 342, 41922, ...
Amicable pairs: (34092, 40842), (46242, 55422), (207624, 259448), ...
sigma(34092) = 86268, phi(34092) = 11352, tau(34092) = 18 and 86268 - 11352 + 18 - 34092 = 40842.
sigma(40842) = 88530, phi(40842) = 13608, tau(40842) = 12 and 88530 - 13608 + 12 - 40842 = 34092.

Maple

with(numtheory); P:=proc(q)local a, n;
for n from 1 to q do a:=sigma(n)-phi(n)+tau(n)-n;
if a>0 and sigma(a)-phi(a)+tau(a)-a=n then print(n);
fi; od; end: P(10^6);

Mathematica

f[n_] := If[n > 0, DivisorSigma[1, n] - EulerPhi[n] + DivisorSigma[0, n] - n, 0]; s={}; Do[ If[f[f[n]] == n, AppendTo[s, n]], {n, 1, 60000}]; s (* Amiram Eldar, Mar 31 2019 *)

Crossrefs

Cf. A000005, A000010, A000203.

Cf. A238225, A238226, A238227, A238228, A238230.

Sequence in context: A009336 A274520 A337616 * A192377 A286344 A279153

Adjacent sequences: A238226 A238227 A238228 * A238230 A238231 A238232

Keyword

nonn

Author

Paolo P. Lava, Feb 20 2014

Extensions

a(11)-a(29) from Amiram Eldar, Mar 31 2019

a(30) from Giovanni Resta, Apr 04 2019

Status

approved