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

Author

Charles R Greathouse IV, Oct 13 2015

Keywords

• nonn

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.

Crossrefs

Intersection of A039770 and A005117.

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

Programs

Magma

[n: n in [1..1400] | IsSquarefree(n) and IsSquare(EulerPhi(n))]; // Vincenzo Librandi, May 05 2016

Mathematica

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

PARI

is(n)=my(f=factor(n)); issquare(eulerphi(f)) && (n==1 || vecmax(f[,2])==1)

Formula

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