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

1,1

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

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.

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