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A054756 Numbers k such that phi(k) and cototient(k) are squares but k is not in A054755. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 19 16:49 EST 2022. Contains 350466 sequences. (Running on oeis4.)