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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 (list; graph; refs; listen; history; text; internal format)
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 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 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

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Last modified August 26 03:38 EDT 2019. Contains 326324 sequences. (Running on oeis4.)