A054756 - OEIS

%I #15 Feb 23 2020 04:49:02

%S 1,468,1417,1872,2340,3145,4100,4212,7488,9360,14841,15588,16400,

%T 16848,20329,21060,29952,31417,37440,37908,45097,49833,58500,62352,

%U 63529,63945,65600,67392,69700,78625,79092,83569,84169,84240,88929,102500

%N Numbers k such that phi(k) and cototient(k) are squares but k is not in A054755.

%H Amiram Eldar, <a href="/A054756/b054756.txt">Table of n, a(n) for n = 1..1000</a>

%F phi(a(n)) = x^2, a(n) - phi(a(n)) = y^2, a(n) is not an odd power of prime from A002496.

%e An even term is 2340 = 4*9*5*13 (phi = 576 = 24^2 and cototient = 1764 =  42^2).

%e An odd term is 14841 = 9*17*97 (phi = 9216 = 96^2, cototient = 5625 = 75^2).

%t Select[ Range[ 1, 200000 ], IntegerQ[ Sqrt[ eu[ # ] ] ]&& IntegerQ[ Sqrt[ co[ # ] ] ]&&!Equal[ lfi[ # ], 1 ]& ], where eu[ x_ ] =EulerPhi[ x ], co[ x_ ]=x-EulerPhi[ x ] and lfi[ x_ ]=Length[ FactorInteger[ x ] ]

%Y Cf. A000010, A002496, A005574, A039770, A051953.

%Y Equals A054754 \setminus A054755. See also A063752.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 25 2000