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A271983
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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).
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1
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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
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OFFSET
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1,2
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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81 is a term because phi(81) = phi(162) = 54 (= A007366(8)).
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MATHEMATICA
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(* 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]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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