login
Number of distinct prime factors of n-th 5-smooth number.
4

%I #13 Apr 12 2020 13:04:33

%S 0,1,1,1,1,2,1,1,2,2,2,1,2,2,2,1,1,3,1,2,2,2,2,2,2,3,1,2,2,2,1,3,2,2,

%T 2,3,1,1,2,2,3,2,2,3,2,2,2,2,3,1,2,1,3,2,3,2,2,3,2,2,2,2,2,3,3,2,2,1,

%U 3,2,3,1,2,2,2,3,1,3,2,2,3,2,3,3,2,2,1,3,2,2,3,2,2,2,2,3,3,2,3,2,2,3,2,3,2

%N Number of distinct prime factors of n-th 5-smooth number.

%H Amiram Eldar, <a href="/A112758/b112758.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..750 from G. C. Greubel)

%F a(n) = A001221(A051037(n)).

%F a(n) = 3 - 0^A112760(n) - 0^A112761(n) - 0^A112762(n).

%F a(n) <= 3.

%t aa = {}; Do[If[8 n - EulerPhi[30 n] == 0, AppendTo[aa, n]], {n, 1, 100}]; PrimeNu[aa] (* _G. C. Greubel_, May 07 2017 *)

%t PrimeNu[#]&/@Select[Range[2000],Max[FactorInteger[#][[All,1]]]<6&] (* _Harvey P. Dale_, Apr 12 2020 *)

%Y Cf. A001221, A051037, A086412, A112753, A112759, A112760, A112761, A112762.

%K nonn

%O 1,6

%A _Reinhard Zumkeller_, Sep 18 2005