A271983 - OEIS

%I #17 Apr 22 2016 06:03:25

%S 1,11,23,29,31,47,53,81,59,67,71,79,83,103,107,121,127,131,137,139,

%T 149,151,167,173,179,191,197,199,211,223,227,229,239,251,263,269,271,

%U 283,293,343,307,311,317,331,361,347,359,367,373,379,383,389,419,431,439,443,463,467,479,491,499

%N 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).

%C 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.

%C 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, ...

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

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

%t Prepend[Select[

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

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

%Y Cf. A007366, A058340.

%K nonn

%O 1,2

%A _Geoffrey Critzer_, Apr 17 2016

%E Edited by _N. J. A. Sloane_, Apr 22 2016 at the suggestion of _Franklin T. Adams-Watters_.