A054754 - OEIS

%I #23 Mar 22 2020 05:47:51

%S 1,2,5,8,17,32,37,101,125,128,197,257,401,468,512,577,677,1297,1417,

%T 1601,1872,2048,2340,2917,3125,3137,3145,4100,4212,4357,4913,5477,

%U 7057,7488,8101,8192,8837,9360,12101,13457,14401,14841,15377,15588,15877

%N Totient(n) and cototient(n) are squares.

%C Subsequence of A039770, supersequence of A002496.

%C a(n) is an odd power of a prime q = w^2+1, like 4913 = 17^3, where A000010(a(31)) = phi(4913) = 4624 = 68^2 and A051953(4913) = 4913-4624 = 289 = 17^2.

%C a(n) is not an odd power of a prime of A002496, like a(14) = 468, where phi(468) = 144 and 468-phi(468) = 324 = 18^2.

%C Intersection of A039770 and A063752. - _Altug Alkan_, Aug 16 2017

%H Donovan Johnson, <a href="/A054754/b054754.txt">Table of n, a(n) for n = 1..10000</a>

%F A000010(a(n))=x^2 and a(n)-A000010(a(n))=y^2.

%t Select[Range@ 16000, Function[n, AllTrue[{#, n - #} &@ EulerPhi@ n, IntegerQ@ Sqrt@ # &]]] (* _Michael De Vlieger_, Aug 16 2017 *)

%o (PARI) isok(n) = issquare(eulerphi(n)) && issquare(n-eulerphi(n)); \\ _Michel Marcus_, Sep 09 2013

%Y Cf. A000010, A002496, A039770, A051953, A063752.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 25 2000