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%I #21 Jan 09 2025 02:54:12
%S 1,259,1260,2071,2834,7574,7749,9252,12800,18720,28236,30039,32724,
%T 42120,45395,45877,68124,102656,135813,246543,264440,341288,389455,
%U 423163,480624,523775,936471,937248,1055954,1182104,1295749,1333626,1366632,1379196,1458270,1483118
%N Numbers k such that the product of Euler phi of the 2 consecutive integers {k,k+1} is a 4th power: if sqrt(sqrt(phi(k)*phi(k+1))) is an integer, then k is here.
%H Amiram Eldar, <a href="/A082788/b082788.txt">Table of n, a(n) for n = 1..300</a> (terms 1..40 from Vincenzo Librandi)
%e k = 937248: phi(k) = 288000, phi(k+1) = 933120, 288000*933120 = 268738560000 = 720^4, so 937248 is here.
%t f[x_] := EulerPhi[x]; Do[s=Sqrt[Sqrt[f[n+1]*f[n]]]; If[IntegerQ[s], Print[n]], {n, 1, 1000000}]
%o (PARI) isok(n) = ispower(eulerphi(n)*eulerphi(n+1), 4); \\ _Michel Marcus_, Jun 15 2017
%K nonn
%O 1,2
%A _Labos Elemer_, May 21 2003
%E a(29)-a(36) from _Vincenzo Librandi_, Jun 15 2017