A067126 - OEIS

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

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OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

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).

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 *)

CROSSREFS

Sequence in context: A327782 A000430 A166684 * A274197 A286267 A337334

Adjacent sequences: A067123 A067124 A067125 * A067127 A067128 A067129

KEYWORD

easy,nonn,changed

AUTHOR

Amarnath Murthy, Jan 09 2002

EXTENSIONS

Offset changed by Andrew Howroyd, Sep 17 2024

STATUS

approved