%I #9 Aug 28 2019 10:35:02

%S 1,2,2,6,6,6,6,864,864,10,10,864,864,864,864,864,864,864,864,20,20,22,

%T 22,864,864,864,864,864,864,864,864,864,864,864,864,864,864,864,864,

%U 864,864,864,864,48,864,46,46,48,864,864,48,864,864,48,48,48,48,58,58

%N Fixed point when phi(sigma(n)+phi(n))=A077080 is iterated with initial value of n.

%C A065387 when iterated seems to converge [tested for initial values below 1024]. On the other hand iterating A051682 often ends in cycle.

%C Iteration of phi(A065387())=phi(sigma()+phi()) seems to converge. Tested below n=1024. Critical values however arise. For example: n=534,556,557,580,624,702,710, etc. These initial values generate very large terms and i was unable to decide if they converge.

%C For n=1..1024 no more but 27 distinct fixed points arised:{1,2,6,10,..,3552,570240}

%F a(n) = FixedPoint[A077080, n].

%e n=225: results in iteration sequence of 44 terms: {225,522,444,...,471744,653312,570240}, a[25]=570240.

%t f[x_] := EulerPhi[DivisorSigma[1, x]+EulerPhi[x]] Table[FixedPoint[f, w], {w, 1, 256}]

%Y Cf. A000010, A000203, A065387, A077080, A077082, A077083, A077084, A077085.

%K nonn

%O 1,2

%A _Labos Elemer_, Oct 28 2002