A114077 Numbers k such that phi(k)*sigma(k) is a cube.

1, 3, 119, 357, 2522, 6305, 6596, 6604, 7566, 18915, 19788, 19812, 20520, 24347, 24353, 26068, 26082, 28126, 47959, 58520, 64790, 65205, 70315, 73041, 73059, 73636, 75460, 78204, 84378, 143877, 156519, 164920, 175560, 194370, 210945, 212660, 220908, 226380

Offset: 1

Author

Giovanni Resta, Feb 13 2006

Keywords

• nonn

Examples

			phi(357) * sigma(357) = 110592 = 48^3.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 119, p. 41, Ellipses, Paris 2008.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..6000

Crossrefs

Cf. A062354.

Programs

Magma

[k:k in [1..230000]| IsPower(EulerPhi(k)*DivisorSigma(1,k),3)]; // Marius A. Burtea, Sep 19 2019

Mathematica

Select[Range[10^5], IntegerQ @ Surd[EulerPhi[#] * DivisorSigma[1, #], 3] &] (* Amiram Eldar, Sep 19 2019 *)

PARI

isok(n) = ispower(eulerphi(n)*sigma(n), 3); \\ Michel Marcus, Jan 22 2014