A306882 Even numbers k such that phi(m) = k^2 has no solution.

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

Offset: 1

Author

Bernard Schott, Mar 15 2019

Keywords

• nonn

Comments

In the link, P. Pollack and C. Pomerance "show that almost all squares are missing from the range of Euler's phi-function".

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.

Includes 2*p if p is a prime not in A052291. - Robert Israel, Apr 10 2019

Examples

			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.
		

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 403-414.

Crossrefs

Cf. A000010, A002202, A052291, A058277, A062732, A221284, A221285.

Programs

Maple

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

PARI

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