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A039771
Numbers k such that phi(k) is a perfect cube.
18
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
OFFSET
1,2
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
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..2500 from E. Pérez Herrero)
EXAMPLE
phi(247) = 216 = 6*6*6.
MATHEMATICA
Select[ Range[ 2000 ], IntegerQ[ Power[ EulerPhi[ # ], 1/3 ] ]& ]
PROG
(PARI) for(n=1, 1e4, if(ispower(eulerphi(n), 3), print1(n", "))) \\ Charles R Greathouse IV, Jul 31 2011
CROSSREFS
KEYWORD
nonn
STATUS
approved