A053034 Length of sequence when A051953 (cototient function) is repeatedly applied starting with n!.

2, 3, 5, 7, 10, 13, 17, 20, 24, 32, 36, 40, 50, 55, 59, 63, 72, 78, 87, 101, 103, 114, 107, 112, 135, 151, 160, 167, 164, 188, 179, 184, 208, 219, 220, 230, 260, 241, 266, 273, 261, 298, 311, 313, 321, 338, 342, 340, 367, 377, 389, 374, 410, 410, 438, 436, 457

Offset

1,1

Comments

The iteration is much slower than the analog for the divisor function; this sequence is not monotonic, cf. A053475.

Links

Table of n, a(n) for n=1..57.

Formula

a(n)-1 is the smallest number such that Nest[cototient, n!, a(n)]=0, the fixed point.

Example

n=8: initial value = 8! = 40320; the successive iterates when cototient is iterated are {40320, 31104, 20736, 13824, 9216, 6144, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0}. Observe the parameters: length=20, cototient was applied 19 times, number of initial non-powers of 2 is 6 and 0 is the 7th, while 13 terminal powers of 2 did arise: 4096, ..., 2, 1.

Mathematica

a[n_] := Module[{c = 1, x = n!}, While[x != 0, x = x - EulerPhi[x]; c++; ]; c]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006 *)

Crossrefs

Cf. A051953, A053475.

Sequence in context: A194238 A364090 A270192 * A029707 A175092 A265250

Adjacent sequences: A053031 A053032 A053033 * A053035 A053036 A053037

Keyword

nonn

Author

Labos Elemer, Feb 24 2000

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006

Status

approved