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A221284 Numbers n such that phi(m) = n^2 for some m. 5
1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 24, 26, 28, 30, 32, 36, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 66, 68, 70, 72, 74, 80, 84, 88, 90, 94, 96, 100, 104, 108, 110, 112, 114, 116, 120, 124, 126, 128, 130, 132, 134, 136, 140, 144, 146, 148, 150, 156, 160, 162, 168, 170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

W. D. Banks, J. B. Friedlander, C. Pomerance, and I. E. Shparlinski, Multiplicative structure of values of the Euler function, in High primes and misdemeanours: Lectures in honour of the sixtieth birthday of Hugh Cowie Williams, Fields Inst. Comm. 41 (2004), pp. 29-47.

Paul Pollack and Carl Pomerance, Square values of Euler's function, Bulletin of the London Mathematical Society 46:2 (April 2014), pp. 403-414.

FORMULA

a(n) = sqrt(A221285(n)).

Pollack and Pomerance show that n (log n)^0.0063 << a(n) << n (log n)^3.

MATHEMATICA

inversePhiSingle[(m_)?EvenQ] := Module[{p, nmax, n}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m*Times @@ (p/(p-1)); n = m; While[n <= nmax, If[EulerPhi[n] == m, Return[n]]; n++]; 0];

Reap[For[k = 1, k <= 200, k = k + If[k==1, 1, 2], If[inversePhiSingle[k^2] > 0, Print[k]; Sow[k]]]][[2, 1]] (* Jean-Fran├žois Alcover, Dec 11 2018 *)

PROG

(PARI) is(n)=istotient(n^2)

CROSSREFS

Cf. A002202, A221285.

Sequence in context: A064720 A029741 A240171 * A272670 A234521 A085125

Adjacent sequences:  A221281 A221282 A221283 * A221285 A221286 A221287

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Feb 05 2013

STATUS

approved

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Last modified May 18 19:29 EDT 2021. Contains 344002 sequences. (Running on oeis4.)