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

1,2

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}

Links

Table of n, a(n) for n=1..59.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A140219 A259225 A300951 * A084700 A122766 A291185

Adjacent sequences: A077078 A077079 A077080 * A077082 A077083 A077084

Keyword

nonn

Author

Labos Elemer, Oct 28 2002

Status

approved