A067126 Numbers for which phi(n) >= phi(k) for all k = 1 to n-1.

1, 2, 3, 4, 5, 7, 9, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269

Offset: 1

Author

Amarnath Murthy, Jan 09 2002

Keywords

• easy
• nonn

Comments

Conjecture: 4 and 9 are the only composite terms.

No more composite terms below 1.5e18. Such a term would require a prime gap greater than sqrt(p); in the absence of such large gaps, a(n) = prime(n-2) for n > 6. - Charles R Greathouse IV, Apr 12 2010

Examples

			4 is a term as phi(4)=2 and phi(1), phi(2), phi(3) are <= 2. 16 is not a term as phi(16) < phi(11).
		

Programs

Mathematica

Join[{1,2,3,4,5,7,9},DeleteDuplicates[Table[{n,EulerPhi[n]},{n,11,280}],GreaterEqual[#1[[2]],#2[[2]]]&][[;;,1]]]  (* Harvey P. Dale, Feb 12 2025 *)

Extensions

Offset changed by Andrew Howroyd, Sep 17 2024