A068796 Maximum k such that k consecutive integers starting at n have distinct numbers of prime factors (counted with multiplicity).

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, 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, 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

Offset

1,1

Comments

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

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

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.

Mathematica

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]]]
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 *)

Crossrefs

Cf. A001222, A067665, A068797.

Sequence in context: A025807 A120254 A263020 * A154804 A207642 A053276

Adjacent sequences: A068793 A068794 A068795 * A068797 A068798 A068799

Keyword

nonn

Author

Dean Hickerson, Mar 05 2002

Status

approved