A060609 Repeatedly apply Euler phi to n-th prime; a(n) = highest power of 2 that is seen.

2, 2, 4, 2, 4, 4, 16, 2, 4, 4, 8, 4, 16, 4, 4, 8, 4, 16, 8, 8, 8, 8, 16, 16, 32, 16, 32, 8, 4, 16, 4, 16, 64, 8, 8, 16, 16, 2, 16, 8, 16, 16, 8, 64, 8, 16, 16, 8, 16, 8, 16, 32, 64, 16, 256, 16, 16, 8, 16, 32, 8, 16, 32, 32, 32, 16, 32, 32, 8, 16, 64, 16, 32, 32, 4, 8, 64, 32, 64, 128

Offset: 1

Author

Labos Elemer, Apr 13 2001

Keywords

• easy
• nonn
• changed

Examples

			n=100,p(100)=541, Phi-iteration chain is {541,540,144,48,16,8,4,2,1} with 9 terms. The largest power of 2 is the 5th term=16=a(100).
		

Links

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

Crossrefs

Cf. A000040, A000010, A049108, A049113, A049116, A003434.

Programs

Mathematica

Table[Max[Select[NestWhileList[EulerPhi[#]&,Prime[n],#>1&],IntegerQ[Log2[#]]&]],{n,80}] (* Harvey P. Dale, Aug 23 2025 *)

Formula

a(n) = A049116(A000040(n)).