A053045 a(n) is the number of powers of 2 among the iterates of the Euler phi function when it is iterated with initial value n!.

1, 2, 2, 4, 6, 7, 8, 11, 11, 14, 17, 19, 21, 23, 25, 29, 33, 34, 35, 39, 40, 44, 48, 51, 55, 58, 58, 61, 64, 67, 70, 75, 78, 83, 86, 88, 90, 92, 94, 99, 104, 106, 108, 113, 115, 120, 125, 129, 131, 136, 140, 144, 148, 149, 154, 158, 159, 163, 167, 171, 175, 179, 180

Offset

1,2

Comments

Powers of 2 arise at the end of iterations without interruption. Analogous to A053035.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Michael De Vlieger)

Formula

a(n) = A049113(n!). - R. J. Mathar, Jan 09 2017

Example

For n = 10, the initial value is 10! = 3628800 and the iteration chain is {3628800, 829440, 221184, 73728, 24576, 8192, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1}. Its length is 19 and 14 values are powers of 2: 8192, ..., 1. Thus a(10) = 14.

Maple

A053045 := proc(n)
    local a, e;
    e := n! ;
    a :=0 ;
    while e > 1 do
        if isA000079(e) then
            a := a+1 ;
        end if;
        e := numtheory[phi](e) ;
    end do:
    1+a;
end proc:
seq(A053045(n), n=1..18) ; # R. J. Mathar, Jan 09 2017

Mathematica

Table[Count[NestWhileList[EulerPhi, n!, # > 1 &], _?(IntegerQ@ Log2@ # &)], {n, 63}] (* Michael De Vlieger, Aug 15 2017 *)

Crossrefs

Cf. A000010, A000142, A049113, A053035.

Sequence in context: A162608 A143216 A086536 * A152424 A145804 A227560

Adjacent sequences: A053042 A053043 A053044 * A053046 A053047 A053048

Keyword

nonn

Author

Labos Elemer, Feb 25 2000

Status

approved