A271983 - OEIS

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A271983

The smaller of a pair n, m such that phi(n) = phi(m) and there is no other k such that phi(n) = phi(k).

1, 11, 23, 29, 31, 47, 53, 81, 59, 67, 71, 79, 83, 103, 107, 121, 127, 131, 137, 139, 149, 151, 167, 173, 179, 191, 197, 199, 211, 223, 227, 229, 239, 251, 263, 269, 271, 283, 293, 343, 307, 311, 317, 331, 361, 347, 359, 367, 373, 379, 383, 389, 419, 431, 439, 443, 463, 467, 479, 491, 499

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

If phi(x) = N has exactly two solutions, x = n and x = m, say (see A007366), it is conjectured that one of n and m is odd and the other even.

This sequence differs from A058340 in that it contains nonprime integers. The first few are 81, 121, 343, 361, 529, 649, 841, 961, 1219, 1331, 1537, 1633, ...

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

81 is a term because phi(81) = phi(162) = 54 (= A007366(8)).

MATHEMATICA

(* takes about 2 minutes, can return the sequence up to terms less than 5760=Euler phi(13 primorial) *)

Prepend[Select[

Table[Flatten[Position[Table[EulerPhi[n], {n, 1, 30030}], m]], {m,

2, 500, 2}], Length[#] == 2 &][[All, 1]], 1]

CROSSREFS

Cf. A007366, A058340.

Sequence in context: A086102 A058340 A138537 * A136000 A054723 A109981