A112758 Number of distinct prime factors of n-th 5-smooth number.

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, 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, 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

Offset

1,6

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..750 from G. C. Greubel)

Formula

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

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

a(n) <= 3.

Mathematica

aa = {}; Do[If[8 n - EulerPhi[30 n] == 0, AppendTo[aa, n]], {n, 1, 100}]; PrimeNu[aa]  (* G. C. Greubel, May 07 2017 *)
PrimeNu[#]&/@Select[Range[2000], Max[FactorInteger[#][[All, 1]]]<6&] (* Harvey P. Dale, Apr 12 2020 *)

Crossrefs

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

Sequence in context: A106032 A003646 A201503 * A029437 A227908 A240473

Adjacent sequences: A112755 A112756 A112757 * A112759 A112760 A112761

Keyword

nonn

Author

Reinhard Zumkeller, Sep 18 2005

Status

approved