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

1,2

Links

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

Formula

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

Example

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).

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 ] ]

Crossrefs

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

Equals A054754 \setminus A054755. See also A063752.

Sequence in context: A221238 A114135 A043364 * A205415 A205408 A282116

Adjacent sequences: A054753 A054754 A054755 * A054757 A054758 A054759

Keyword

nonn

Author

Labos Elemer, Apr 25 2000

Status

approved