A124830 - OEIS

%I #27 May 08 2021 06:30:04

%S 0,1,1,2,1,2,1,2,2,3,1,2,2,2,3,1,2,3,2,2,3,1,2,3,2,3,2,4,2,3,1,3,2,3,

%T 2,3,2,4,2,3,3,2,1,3,2,3,4,2,3,3,2,3,4,2,3,3,2,1,4,3,2,3,4,2,3,3,2,4,

%U 3,2,3,4,2,3,4,3,2,1,4,3,3,2,5,3,3,4,2,3,3,2,4,3,2,4,3,4,2,3,3,4,3,2,3,1,4

%N Number of distinct prime factors of A055932(n).

%H Michael De Vlieger, <a href="/A124830/b124830.txt">Table of n, a(n) for n = 1..10000</a> (First 1000 terms from G. C. Greubel.)

%F a(n) = A001221(A055932(n)).

%t PrimeNu /@ Select[Range[4000], ! MemberQ[Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ #, 0] &] (* _Michael De Vlieger_, Feb 02 2017 *)

%t A055932[n_] := Module[{f = Transpose[FactorInteger[n]][[1]]}, f == {1} || f == Prime[Range[Length[f]]]]; PrimeNu[Select[Range[2000], A055932]] (* _G. C. Greubel_, May 11 2017 *)

%o (Python)

%o from sympy import nextprime, primefactors

%o def a053669(n):

%o     p = 2

%o     while True:

%o         if n%p!=0: return p

%o         else: p=nextprime(p)

%o def ok(n): return True if n==1 else a053669(n)>max(primefactors(n))

%o print([len(primefactors(n)) for n in range(1, 10001) if ok(n)]) # _Indranil Ghosh_, May 11 2017

%Y Cf. A055932, A001221, A124829, A124831, A061394.

%K nonn

%O 1,4

%A _Franklin T. Adams-Watters_, Nov 09 2006