

A306882


Even numbers k such that phi(m) = k^2 has no solution.


2



22, 34, 38, 46, 58, 62, 76, 78, 82, 86, 92, 98, 102, 106, 118, 122, 138, 142, 152, 154, 158, 164, 166, 172, 178, 182, 190, 194, 202, 212, 214, 218, 226, 238, 244, 254, 258, 262, 266, 274, 278, 282, 298, 302, 304, 310, 316, 318, 322, 328, 332, 334, 338, 344, 346, 356, 358, 362
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OFFSET

1,1


COMMENTS

In the link, P. Pollack and C. Pomerance "show that almost all squares are missing from the range of Euler's phifunction".
Except for m=1 and m=2, phi(m) is always even, so, the odd numbers >= 3 are not proposed in the data for clarity.
Includes 2*p if p is a prime not in A052291.  Robert Israel, Apr 10 2019


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
P. Pollack and C. Pomerance, Square values of Euler's function, preprint (2013); Bulletin of the London Mathematical Society, Volume 46, Issue 2, 1 April 2014, Pages 403414.


EXAMPLE

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.


MAPLE

select(t > numtheory:invphi(t^2)=[], [seq(i, i=2..400, 2)]); # Robert Israel, Apr 10 2019


PROG

(PARI) isok(n) = !(n%2) && !istotient(n^2); \\ Michel Marcus, Mar 15 2019


CROSSREFS

Cf. A000010, A002202, A052291, A058277, A062732, A221284, A221285.
Sequence in context: A071265 A213974 A103320 * A125526 A181177 A124317
Adjacent sequences: A306879 A306880 A306881 * A306883 A306884 A306885


KEYWORD

nonn


AUTHOR

Bernard Schott, Mar 15 2019


STATUS

approved



