A064375 Numbers n such that sigma_2(n) > phi(n)^3.

2, 3, 4, 6, 8, 10, 12, 14, 18, 20, 24, 30, 36, 42, 60

Offset: 1

Author

Labos Elemer, Sep 27 2001

Keywords

• nonn
• fini

Comments

This sequence is finite, since by Grönwall's theorem sigma_2(n) <= sigma(n)^2 << (n log log n)^2 but phi(n)^3 >> (n/log log n)^3. - Charles R Greathouse IV, Nov 18 2015

Examples

			d-square sums:{5, 10, 21, 50, 85, 130, 210, 250, 455, 546, 850, 1300, 1911, 2500, 5460} phi-cubes:{1, 8, 8, 8, 64, 64, 64, 216, 216, 512, 512, 512, 1728, 1728, 4096} differences:{4, 2, 13, 42, 21, 66, 146, 34, 239, 34, 338, 788, 183, 772, 1364} Sequence is believed to be full.
		

Crossrefs

Cf. A001157, A000010, A055234.

Programs

Mathematica

Select[Range[100],DivisorSigma[2,#]>EulerPhi[#]^3&] (* Harvey P. Dale, Feb 19 2013 *)

PARI

is(n)=my(f=factor(n)); sigma(f,2)>eulerphi(f)^3 \\ Charles R Greathouse IV, Nov 18 2015

Formula

Solutions to A001157(n) > A000010(x)^3.