A082788 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.

1, 259, 1260, 2071, 2834, 7574, 7749, 9252, 12800, 18720, 28236, 30039, 32724, 42120, 45395, 45877, 68124, 102656, 135813, 246543, 264440, 341288, 389455, 423163, 480624, 523775, 936471, 937248, 1055954, 1182104, 1295749, 1333626, 1366632, 1379196, 1458270, 1483118

Offset: 1

Author

Labos Elemer, May 21 2003

Keywords

• nonn

Examples

			k = 937248: phi(k) = 288000, phi(k+1) = 933120, 288000*933120 = 268738560000 = 720^4, so 937248 is here.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..300 (terms 1..40 from Vincenzo Librandi)

Programs

Mathematica

f[x_] := EulerPhi[x]; Do[s=Sqrt[Sqrt[f[n+1]*f[n]]]; If[IntegerQ[s], Print[n]], {n, 1, 1000000}]

PARI

isok(n) = ispower(eulerphi(n)*eulerphi(n+1), 4); \\ Michel Marcus, Jun 15 2017

Extensions

a(29)-a(36) from Vincenzo Librandi, Jun 15 2017