A049116 Repeatedly apply Euler phi to n; a(n) = highest power of 2 that is seen.

1, 2, 2, 4, 4, 2, 2, 8, 2, 4, 4, 4, 4, 2, 8, 16, 16, 2, 2, 8, 4, 4, 4, 8, 8, 4, 2, 4, 4, 8, 8, 32, 8, 16, 8, 4, 4, 2, 8, 16, 16, 4, 4, 8, 8, 4, 4, 16, 4, 8, 32, 8, 8, 2, 16, 8, 4, 4, 4, 16, 16, 8, 4, 64, 16, 8, 8, 32, 8, 8, 8, 8, 8, 4, 16, 4, 16, 8, 8, 32, 2, 16, 16, 8, 64, 4, 8, 16, 16, 8, 8, 8

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

If n is a power of 2, then it is of largest exponent. If n=2400, then its phi-sequence is {2400,640,256,128,64,32,16,8,4,2,1}. The value of first power of 2 is 256. Thus a(2400)=256.

Mathematica

Table[SelectFirst[NestWhileList[EulerPhi[#]&, n, #>1&], IntegerQ[Log[2, #]]&], {n, 120}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 23 2019 *)

Crossrefs

Cf. A000010.

Sequence in context: A325445 A165207 A130501 * A065176 A368558 A060267

Adjacent sequences: A049113 A049114 A049115 * A049117 A049118 A049119

Keyword

nonn

Author

Labos Elemer

Status

approved