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%I #13 May 13 2017 03:43:12
%S 7,9,11,13,19,23,25,27,29,31,37,41,43,47,49,53,59,61,62,67,71,73,77,
%T 79,81,83,86,89,93,97,98,99,101,103,107,109,113,121,122,124,125,127,
%U 129,131,134,137,139,142,143,147,149,151,155,157,158,161,163,167,169,172
%N Phi(n) has more distinct prime factors than n.
%C Conjecture: a(n) ~ n. - _Charles R Greathouse IV_, Mar 04 2017
%H Charles R Greathouse IV, <a href="/A055741/b055741.txt">Table of n, a(n) for n = 1..10000</a>
%F A001221(A000010(n)) > A001221(n)
%e All primes except Fermat primes are included. Also proper prime powers are included, such as 289 because phi(289) = 17*16 = 272 with 2 prime divisors. Besides many composites are included like 998 = 2*499 because phi(998) = 498 = 2*3*83 with 3 > 2 prime factors.
%t Select[Range[100], PrimeNu[EulerPhi[#]] > PrimeNu[#] &] (* _G. C. Greubel_, May 13 2017 *)
%o (PARI) is(n)=my(f=factor(n)); omega(eulerphi(f)) > #f~ \\ _Charles R Greathouse IV_, Mar 04 2017
%Y Cf. A001221, A000010, A055742, A055743.
%K nonn
%O 1,1
%A _Labos Elemer_, Jul 11 2000
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