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Composite numbers k+1 such that k*phi(k+1) is a perfect square.
1

%I #14 Apr 30 2022 08:21:20

%S 9,27,50,169,242,245,945,1127,1280,1352,1694,2430,4335,4410,4624,4802,

%T 7500,7935,8624,11913,12544,13254,15050,16384,24642,27869,29403,31827,

%U 33489,36750,39675,47045,52800,53290,55470,58806,66248,72075,74060,81675,90774,90972

%N Composite numbers k+1 such that k*phi(k+1) is a perfect square.

%C Trivially if k+1 is prime k*phi(k+1) = k^2. If k>1 k*phi(k) is never a perfect square.

%H Amiram Eldar, <a href="/A069068/b069068.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[60000], !PrimeQ[ #+1] && IntegerQ[Sqrt[ # EulerPhi[1+# ]]]&] (* _T. D. Noe_, Nov 01 2006 *)

%Y Cf. A000010, A000290.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Apr 05 2002

%E Corrected by _T. D. Noe_, Nov 01 2006

%E More terms from _Amiram Eldar_, Apr 29 2022