A077081 Fixed point when phi(sigma(n)+phi(n))=A077080 is iterated with initial value of n.

1, 2, 2, 6, 6, 6, 6, 864, 864, 10, 10, 864, 864, 864, 864, 864, 864, 864, 864, 20, 20, 22, 22, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 864, 48, 864, 46, 46, 48, 864, 864, 48, 864, 864, 48, 48, 48, 48, 58, 58

Offset: 1

Author

Labos Elemer, Oct 28 2002

Keywords

• nonn

Comments

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

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.

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

Examples

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

Crossrefs

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

Programs

Mathematica

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

Formula

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