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A053038 The first (largest) power of 2 arising in the iteration-sequence when A051953 (the cototient function) is repeatedly applied starting with n!. 2
1, 2, 4, 16, 32, 128, 512, 4096, 16384, 2048, 8192, 65536, 16384, 65536, 8388608, 134217728, 8388608, 8388608, 16777216, 2097152, 8388608, 268435456, 4398046511104, 70368744177664, 67108864, 67108864, 67108864, 68719476736 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..28.

EXAMPLE

For n = 10, initial value = 10! = 3628800; after the following initial terms {3628800, 2799360, 2052864, 1430784, 974592, 656640, 490752, 329472,  237312, 158976, 108288, 72960, 54528, 36608, 21248, 10752, 7680, 5632, 3072, ...}, the first power of 2 is 2048 = cototient(3072). Therefore a(10) = 2048.

MATHEMATICA

Table[NestWhile[# - EulerPhi@ # &, n!, ! IntegerQ@ Log2@ # &], {n, 28}] (* Michael De Vlieger, Aug 15 2017 *)

CROSSREFS

Cf. A051953, A053475, A053039.

Sequence in context: A081411 A269758 A094384 * A001088 A101926 A087965

Adjacent sequences:  A053035 A053036 A053037 * A053039 A053040 A053041

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 24 2000

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)