A262406 Squarefree k such that phi(k) is a perfect square.

1, 2, 5, 10, 17, 34, 37, 57, 74, 85, 101, 114, 170, 185, 197, 202, 219, 257, 273, 285, 370, 394, 401, 438, 451, 489, 505, 514, 546, 570, 577, 629, 677, 679, 802, 902, 969, 978, 985, 1010, 1057, 1095, 1154, 1258, 1285, 1297, 1354, 1358, 1365

Offset

1,2

Comments

The subsequence of primes is A002496 (primes of the form k^2+1). - Michel Marcus, Oct 14 2015

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 (A. Van der Poorten, ed.), Fields Inst. Comm. 41 (2004), pp. 29-47.

Formula

Banks, Friedlander, Pomerance, and Shparlinski show that a(n) = O(n^1.421).

Mathematica

Select[Range[1500], SquareFreeQ[#] && IntegerQ @ Sqrt @ EulerPhi[#] &] (* Amiram Eldar, Jul 16 2022 *)

Prog

(PARI) is(n)=my(f=factor(n)); issquare(eulerphi(f)) && (n==1 || vecmax(f[, 2])==1)
(Magma) [n: n in [1..1400] | IsSquarefree(n) and IsSquare(EulerPhi(n))]; // Vincenzo Librandi, May 05 2016

Crossrefs

Intersection of A039770 and A005117.

Cf. A000010, A002496, A007614, A068560, A004171, A114063.

Sequence in context: A227363 A372683 A342172 * A308600 A308604 A018315

Adjacent sequences: A262403 A262404 A262405 * A262407 A262408 A262409

Keyword

nonn

Author

Charles R Greathouse IV, Oct 13 2015

Status

approved