OFFSET
1,2
COMMENTS
Contains {2*3^(6k+1): k >= 1} as a subsequence. This is the simplest proof for the infinity of these numbers (see Sierpiński, Exercise 12, p. 237). - Franz Vrabec, Aug 21 2021
The smaller of the solutions to phi(x) = a(n) is given by A271983(n). It is conjectured that the larger solution is 2*A271983(n); or equivalently, all terms in A271983 are odd. - Jianing Song, Nov 08 2022
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
W. Sierpiński, Elementary Theory of Numbers, Warszawa, 1964.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
R. G. Wilson v, Letter to N. J. A. Sloane, Jul. 1992
FORMULA
#({phi^-1(a(n))}) = 2. - Torlach Rush, Dec 22 2017
EXAMPLE
10 = phi(11) = phi(22).
MAPLE
select(nops@numtheory:-invphi=2, [$1..1000]); # Robert Israel, Dec 20 2017
MATHEMATICA
a = Table[ 0, {500} ]; Do[ p = EulerPhi[ n ]; If[ p < 501, a[ [ p ] ]++ ], {n, 1, 500} ]; Select[ Range[ 500 ], a[ [ # ] ] == 2 & ]
(* Second program: *)
With[{nn = 1325}, TakeWhile[Union@ Select[KeyValueMap[{#1, Length@ #2} &, PositionIndex@ Array[EulerPhi, nn]], Last@ # == 2 &][[All, 1]], # < nn/3 &] ] (* Michael De Vlieger, Dec 20 2017 *)
CROSSREFS
KEYWORD
nonn
STATUS
approved