A054756 Numbers k such that phi(k) and cototient(k) are squares but k is not in A054755.

1, 468, 1417, 1872, 2340, 3145, 4100, 4212, 7488, 9360, 14841, 15588, 16400, 16848, 20329, 21060, 29952, 31417, 37440, 37908, 45097, 49833, 58500, 62352, 63529, 63945, 65600, 67392, 69700, 78625, 79092, 83569, 84169, 84240, 88929, 102500

Offset: 1

Author

Labos Elemer, Apr 25 2000

Keywords

• nonn

Examples

			An even term is 2340 = 4*9*5*13 (phi = 576 = 24^2 and cototient = 1764 =  42^2).
An odd term is 14841 = 9*17*97 (phi = 9216 = 96^2, cototient = 5625 = 75^2).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

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

Equals A054754 \setminus A054755. See also A063752.

Programs

Mathematica

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 ] ]

Formula

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