A039771 Numbers k such that phi(k) is a perfect cube.

1, 2, 15, 16, 20, 24, 30, 85, 128, 136, 160, 170, 192, 204, 240, 247, 259, 327, 333, 351, 399, 405, 436, 494, 518, 532, 648, 654, 666, 684, 702, 756, 771, 798, 810, 1024, 1028, 1088, 1111, 1255, 1280, 1360, 1375, 1536, 1542, 1632, 1843, 1853, 1875, 1920, 2008

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• changed

Comments

a(n) is prime only for a(2)=2, for other cases: eulerphi(p) = p-1 = n^3, and p = 1 + n^3 = (n+1)(n^2-n+1), so p cannot be a prime. - Enrique Pérez Herrero, Aug 29 2010

A013730 is a subsequence. - Enrique Pérez Herrero, Aug 29 2010

Examples

			phi(247) = 216 = 6*6*6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from E. Pérez Herrero)

Crossrefs

Cf. A000010, A007614, A039770, A216412.

Programs

Maple

q:= n-> (c-> iroot(c, 3)^3=c)(numtheory[phi](n)):
select(q, [$1..2200])[];  # Alois P. Heinz, Sep 01 2025

Mathematica

Select[ Range[ 2000 ], IntegerQ[ Power[ EulerPhi[ # ], 1/3 ] ]& ]

PARI

for(n=1,1e4,if(ispower(eulerphi(n),3),print1(n", "))) \\ Charles R Greathouse IV, Jul 31 2011