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A053035 Number of powers of 2 in the iteration-sequence when A051953 (cototient function) is repeatedly applied starting with n!. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A072190 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

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)