A114078 Numbers k such that phi(k)*sigma(k) is a fourth power.

1, 170, 595, 714, 121056, 480441, 529620, 706063, 706237, 729752, 755972, 815654, 2162808, 2449062, 2827789, 2927848, 2957416, 2994681, 2995419, 3010227, 3019028, 3019772, 3080140, 3093860, 3103464, 3206364, 3213804

Offset: 1

Author

Giovanni Resta, Feb 13 2006

Keywords

• nonn

Examples

			phi(595) * sigma(595) = 331776 = 24^4.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 170, p. 54, Ellipses, Paris 2008.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..600

Crossrefs

Cf. A062354, subsequence of A011257.

Programs

Magma

[k:k in [1..3300000]| IsPower(EulerPhi(k)*DivisorSigma(1,k),4)]; // Marius A. Burtea, Sep 19 2019

Mathematica

Select[Range[3300000],IntegerQ[Power[EulerPhi[#] DivisorSigma[1,#], (4)^-1]]&]  (* Harvey P. Dale, Mar 14 2011 *)

PARI

isok(n) = ispower(eulerphi(n)*sigma(n), 4); \\ Michel Marcus, Jan 09 2014