A053098 When the Euler phi function is iterated with initial value A002110(n)=primorial, a(n)= first (maximal) power of 2 emerging during iteration.

2, 2, 8, 16, 128, 512, 8192, 16384, 262144, 2097152, 16777216, 67108864, 2147483648, 8589934592, 274877906944, 4398046511104, 70368744177664, 1125899906842624, 18014398509481984, 288230376151711744

Offset

1,1

Comments

Analogous to A053047 (the same with a similar large initial value, n!).

Links

Table of n, a(n) for n=1..20.

Example

n=6, A002110(6)=30030; the corresponding iteration chain is {30030, 5760, 1536, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. The first power of 2 is the 4th item after 3 iterations. It is 512, therefore a(6)=512.

Mathematica

a[n_] := 2^ Max@ IntegerExponent[ FixedPointList[ EulerPhi, Times @@ Prime[Range[n]]], 2]; Array[a, 20] (* Giovanni Resta, May 30 2018 *)

Crossrefs

Cf. A000010, A002110.

Sequence in context: A085542 A239682 A009725 * A354117 A194588 A175395

Adjacent sequences: A053095 A053096 A053097 * A053099 A053100 A053101

Keyword

nonn

Author

Labos Elemer, Feb 28 2000

Status

approved