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

1,2

Comments

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

Links

Table of n, a(n) for n=1..71.

Example

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.

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 *)

Crossrefs

Cf. A051953, A053475.

Sequence in context: A356137 A177445 A022826 * A160009 A049862 A022829

Adjacent sequences: A053032 A053033 A053034 * A053036 A053037 A053038

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