A053038 The first (largest) power of 2 arising in the iteration-sequence when A051953 (the cototient function) is repeatedly applied starting with n!.

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

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