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%I #26 Jul 16 2022 07:14:10
%S 1,2,5,10,17,34,37,57,74,85,101,114,170,185,197,202,219,257,273,285,
%T 370,394,401,438,451,489,505,514,546,570,577,629,677,679,802,902,969,
%U 978,985,1010,1057,1095,1154,1258,1285,1297,1354,1358,1365
%N Squarefree k such that phi(k) is a perfect square.
%C The subsequence of primes is A002496 (primes of the form k^2+1). - _Michel Marcus_, Oct 14 2015
%H Charles R Greathouse IV, <a href="/A262406/b262406.txt">Table of n, a(n) for n = 1..10000</a>
%H W. D. Banks, J. B. Friedlander, C. Pomerance and I. E. Shparlinski, <a href="http://math.dartmouth.edu/~carlp/PDF/banksfinal2.pdf">Multiplicative structure of values of the Euler function</a>, 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.
%F Banks, Friedlander, Pomerance, and Shparlinski show that a(n) = O(n^1.421).
%t Select[Range[1500], SquareFreeQ[#] && IntegerQ @ Sqrt @ EulerPhi[#] &] (* _Amiram Eldar_, Jul 16 2022 *)
%o (PARI) is(n)=my(f=factor(n)); issquare(eulerphi(f)) && (n==1 || vecmax(f[,2])==1)
%o (Magma) [n: n in [1..1400] | IsSquarefree(n) and IsSquare(EulerPhi(n))]; // _Vincenzo Librandi_, May 05 2016
%Y Intersection of A039770 and A005117.
%Y Cf. A000010, A002496, A007614, A068560, A004171, A114063.
%K nonn
%O 1,2
%A _Charles R Greathouse IV_, Oct 13 2015
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