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A238230 Numbers m such that if x = sigma(m)-phi(m)-tau(m)-m then m = sigma(x)-phi(x)-tau(x)-x.

%I A238230 #33 Jun 14 2022 08:51:30
%S A238230 198,294,16008,22232,150030,195320,200274,3038720,12190720,124904790,
%T A238230 167179722,347943288,426853240,528995656,646186568,3588779502,
%U A238230 4798752860,5376246738,5898361924,158380893880,189740533470,196271084296,240458641570,375653406648
%N A238230 Numbers m such that if x = sigma(m)-phi(m)-tau(m)-m then m = sigma(x)-phi(x)-tau(x)-x.
%C A238230 All numbers of the form 2^k*5*p, where p = (7*2^k-2*k-5)/3 is prime, are fixed points and thus terms. This happens for k = 9, 10, 124, 352, 1468, 3339, 4365,... - _Giovanni Resta_, Mar 26 2014
%C A238230 The fixed points (terms with x = m) are 198, 294, 195320, 3038720, 12190720, ... - _Amiram Eldar_, Mar 31 2019
%C A238230 a(20) > 10^11. - _Giovanni Resta_, Apr 04 2019
%e A238230 Fixed points: 198, 294, 195320,...
%e A238230 sigma(16008) = 43200, phi(16008) = 4928, tau(16008) = 32 and 43200 - 4928 - 32- 16008 = 22232.
%e A238230 sigma(22232) = 47760, phi(22232) = 9504, tau(22232) = 16 and 47760 - 9504 - 16 - 22232 = 16008.
%p A238230 with(numtheory); P:=proc(q)local a,n;
%p A238230 for n from 1 to q do a:=sigma(n)-phi(n)-tau(n)-n;
%p A238230 if a>0 and sigma(a)-phi(a)-tau(a)-a=n then print(n);
%p A238230 fi; od; end: P(10^6);
%t A238230 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, 200000}]; s (* _Amiram Eldar_, Mar 31 2019 *)
%Y A238230 Cf. A000005, A000010, A000203, A055971, A238225-A238229.
%K A238230 nonn,more
%O A238230 1,1
%A A238230 _Paolo P. Lava_, Feb 20 2014
%E A238230 a(8)-a(15) from _Giovanni Resta_, Mar 26 2014
%E A238230 a(16)-a(19) from _Amiram Eldar_, Mar 31 2019
%E A238230 a(19) corrected by _Kevin P. Thompson_, Jan 12 2022
%E A238230 a(20)-a(23) from _Kevin P. Thompson_, Apr 17 2022
%E A238230 a(24) from _Kevin P. Thompson_, Jun 13 2022