A064376 Numbers n such that sigma_3(n) > phi(n)^4.

2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 30, 36, 40, 42, 48, 54, 60, 66, 70, 72, 78, 84, 90, 102, 114, 120, 126, 132, 150, 168, 180, 210, 330, 420

Offset: 1

Author

Labos Elemer, Sep 27 2001

Keywords

• nonn
• fini

Comments

This sequence is finite, since by Grönwall's theorem sigma_3(n) <= sigma(n)^3 << (n log log n)^3 but phi(n)^4 >> (n/log log n)^4. - Charles R Greathouse IV, Nov 19 2015

Crossrefs

Cf. A001158, A000010.

Programs

Mathematica

Select[Range[500],DivisorSigma[3,#]>EulerPhi[#]^4&] (* Harvey P. Dale, Jun 21 2024 *)

PARI

is(n)=my(f=factor(n)); sigma(f, 3)>eulerphi(f)^4 \\ Charles R Greathouse IV, Nov 19 2015

Formula

Solutions to A001158(n) > phi(n)^4.