A053035 Number of powers of 2 in the iteration-sequence when A051953 (cototient function) is repeatedly applied starting with n!.

1, 2, 3, 5, 6, 8, 10, 13, 15, 12, 14, 17, 15, 17, 24, 28, 24, 24, 25, 22, 24, 29, 43, 47, 27, 27, 27, 37, 44, 30, 51, 56, 38, 38, 41, 41, 40, 60, 40, 45, 69, 43, 43, 45, 52, 46, 51, 54, 50, 53, 52, 86, 56, 58, 54, 58, 61, 86, 63, 72, 63, 64, 61, 67, 67, 108, 68, 102, 77, 71, 76

Offset: 1

Author

Labos Elemer, Feb 24 2000

Keywords

• nonn

Comments

Unlike the analogous sequence with A000005, the powers of 2 which emerge are consecutive iterates.

Examples

			n=7, initial value=7!=5040, the successive iterates when cototient function (A051953) is repeatedly applied are: {5040,3888,2592,1728,1152,768,512,256,128,64,32,16,8,4,2,1,0}. Between the initial segment and terminal 0, ten powers of 2 emerge: 512,...,1. Thus a(7)=10.
		

Crossrefs

Cf. A051953, A053475.

Programs

Mathematica

a[n_] := Module[{x = n!}, While[ ! IntegerQ[Log[2, x]], x = x - EulerPhi[x];]; Log[2, x] + 1]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006 *)

Extensions

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