cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A054756 #15 Feb 23 2020 04:49:02
%S A054756 1,468,1417,1872,2340,3145,4100,4212,7488,9360,14841,15588,16400,
%T A054756 16848,20329,21060,29952,31417,37440,37908,45097,49833,58500,62352,
%U A054756 63529,63945,65600,67392,69700,78625,79092,83569,84169,84240,88929,102500
%N A054756 Numbers k such that phi(k) and cototient(k) are squares but k is not in A054755.
%H A054756 Amiram Eldar, <a href="/A054756/b054756.txt">Table of n, a(n) for n = 1..1000</a>
%F A054756 phi(a(n)) = x^2, a(n) - phi(a(n)) = y^2, a(n) is not an odd power of prime from A002496.
%e A054756 An even term is 2340 = 4*9*5*13 (phi = 576 = 24^2 and cototient = 1764 =  42^2).
%e A054756 An odd term is 14841 = 9*17*97 (phi = 9216 = 96^2, cototient = 5625 = 75^2).
%t A054756 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 A054756 Cf. A000010, A002496, A005574, A039770, A051953.
%Y A054756 Equals A054754 \setminus A054755. See also A063752.
%K A054756 nonn
%O A054756 1,2
%A A054756 _Labos Elemer_, Apr 25 2000