A068796 - OEIS

%I #15 Nov 12 2015 06:04:54

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

%T 3,3,2,1,4,3,2,2,2,1,4,3,4,3,2,2,4,4,3,2,2,2,1,3,2,5,4,3,3,4,3,2,3,2,

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

%N Maximum k such that k consecutive integers starting at n have distinct numbers of prime factors (counted with multiplicity).

%C The number of prime factors (counted with multiplicity) of n is bigomega(n) = A001222(n).

%H Zak Seidov, <a href="/A068796/b068796.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6)=3 because 6, 7, 8 and 9 have, respectively, 2, 1, 3 and 2 prime factors; the first 3 of these are distinct.

%t bigomega[n_] := Plus@@Last/@FactorInteger[n]; a[n_] := For[k=1; s={bigomega[n]}, True, k++, If[MemberQ[s, z=bigomega[n+k]], Return[k], AppendTo[s, z]]]

%t ss={}; Do[s={PrimeOmega[n]};k=1;While[FreeQ[s, (b=PrimeOmega[n+k])],s=AppendTo[s,b];k++];ss=AppendTo[ss,k],{n,103}]; (* _Zak Seidov_, Nov 09 2015 *)

%Y Cf. A001222, A067665, A068797.

%K nonn

%O 1,1

%A _Dean Hickerson_, Mar 05 2002