A238229 - OEIS

%I #26 Jun 14 2022 08:51:35

%S 2,4,20,66,342,34092,40842,41922,46242,55422,207624,259448,533172,

%T 547300,571992,667408,1531032,1786288,10983114,114013752,133506680,

%U 323277822,347360860,386144360,387415458,459603716,476991704,1443279992,1539484232,15537978552

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

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

%H Kevin P. Thompson, <a href="/A238229/b238229.txt">Table of n, a(n) for n = 1..38</a>

%e Fixed points: 2, 4, 20, 66, 342, 41922, ...

%e Amicable pairs: (34092, 40842), (46242, 55422), (207624, 259448), ...

%e sigma(34092) = 86268, phi(34092) = 11352, tau(34092) = 18 and 86268 - 11352 + 18 - 34092 = 40842.

%e sigma(40842) = 88530, phi(40842) = 13608, tau(40842) = 12 and 88530 - 13608 + 12 - 40842 = 34092.

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

%p for n from 1 to q do a:=sigma(n)-phi(n)+tau(n)-n;

%p if a>0 and sigma(a)-phi(a)+tau(a)-a=n then print(n);

%p fi; od; end: P(10^6);

%t 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 *)

%Y Cf. A000005, A000010, A000203.

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

%K nonn

%O 1,1

%A _Paolo P. Lava_, Feb 20 2014

%E a(11)-a(29) from _Amiram Eldar_, Mar 31 2019

%E a(30) from _Giovanni Resta_, Apr 04 2019