A064374 Numbers k such that sigma(k) > phi(k)^2.

2, 4, 6, 10, 12, 18, 30

Offset: 1

Author

Labos Elemer, Sep 27 2001

Keywords

• nonn
• fini
• full

Comments

Also numbers k such that sigma(k) > tau(k)*phi(k). - Benoit Cloitre, Aug 06 2002

There are no further terms. - Benoit Cloitre, Aug 06 2002

Examples

			k = {2, 4, 6, 10, 12, 18, 30};
sigma(k) = {3, 7, 12, 18, 28, 39, 72};
phi(k) = {1, 2, 2, 4, 4, 6, 8};
phi(k)^2 = {1, 4, 4, 16, 16, 36, 64};
sigma(k) - phi(k)^2 = {2, 3, 8, 2, 12, 3, 8}.
No more solutions below 10000000.
		

Crossrefs

Cf. A000010, A000203, A055234.

Programs

Mathematica

Select[Range[30],DivisorSigma[1,#]>EulerPhi[#]^2&] (* Harvey P. Dale, Sep 27 2024 *)

Formula

Solutions to A000203(k) > A000010(k)^2.