A064377 Numbers n such that sigma_4(n) > phi(n)^5.

2, 3, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 48, 50, 54, 56, 60, 66, 70, 72, 78, 80, 84, 90, 96, 100, 102, 108, 110, 114, 120, 126, 130, 132, 138, 140, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 294, 300, 306, 312, 330, 336, 342, 360, 378, 390, 396, 420, 450, 462, 480, 504, 510, 540, 546, 570, 600, 630, 660, 690, 714, 720, 750, 780, 840, 870, 930, 990, 1020, 1050, 1170, 1260, 1470, 1680, 2310

Offset: 1

Author

Labos Elemer, Sep 27 2001

Keywords

• nonn
• fini
• full

Comments

It is conjectured that there are no other solutions.

This sequence is finite, since by Grönwall's theorem sigma_4(n) <= sigma(n)^4 << (n log log n)^4 but phi(n)^5 >> (n/log log n)^5. - Charles R Greathouse IV, Nov 19 2015

Crossrefs

Cf. A001159, A000010.

Programs

Mathematica

Select[Range[2400],DivisorSigma[4,#]>EulerPhi[#]^5&] (* Harvey P. Dale, Aug 20 2021 *)

PARI

is(n)=my(f=factor(n)); sigma(f, 4)>eulerphi(f)^5 \\ Charles R Greathouse IV, Nov 19 2015

Formula

Solutions to A001159(n) > phi(n)^5.