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%I #39 Apr 03 2023 15:16:00
%S 22,34,38,46,58,62,76,78,82,86,92,98,102,106,118,122,138,142,152,154,
%T 158,164,166,172,178,182,190,194,202,212,214,218,226,238,244,254,258,
%U 262,266,274,278,282,298,302,304,310,316,318,322,328,332,334,338,344,346,356,358,362
%N Even numbers k such that phi(m) = k^2 has no solution.
%C In the link, P. Pollack and C. Pomerance "show that almost all squares are missing from the range of Euler's phi-function".
%C Except for m=1 and m=2, phi(m) is always even, so, the odd numbers >= 3 are not included in the data for clarity.
%C Includes 2*p if p is a prime not in A052291. - _Robert Israel_, Apr 10 2019
%H Robert Israel, <a href="/A306882/b306882.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Pollack and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/squaretotients5.pdf">Square values of Euler's function</a>, preprint (2013); Bulletin of the London Mathematical Society, Volume 46, Issue 2, 1 April 2014, Pages 403-414.
%e phi(489) = 18^2, phi(401) = 20^2, phi(577) = 24^2, phi(677) = 26^2, but there is no integer m such that phi(m) = 22^2 = 484.
%p select(t -> numtheory:-invphi(t^2)=[], [seq(i,i=2..400,2)]); # _Robert Israel_, Apr 10 2019
%o (PARI) isok(n) = !(n%2) && !istotient(n^2); \\ _Michel Marcus_, Mar 15 2019
%Y Cf. A000010, A002202, A052291, A058277, A062732, A221284, A221285.
%K nonn
%O 1,1
%A _Bernard Schott_, Mar 15 2019
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