login
The count of smallest prime factors in n-th composite.
1

%I #11 Apr 20 2022 13:36:01

%S 2,1,3,2,1,2,1,1,4,1,2,1,1,3,2,1,3,2,1,5,1,1,1,2,1,1,3,1,2,2,1,4,2,1,

%T 1,2,1,1,3,1,1,2,1,2,6,1,1,2,1,1,3,1,1,2,1,1,4,4,1,2,1,1,1,3,1,1,2,1,

%U 1,1,5,1,2,2,1,3,1,1,2,1,1,4,1,1,2,2,1,1,3,2,1,1,2,3,1,7,1,1,2,1,1,3,3,1,2

%N The count of smallest prime factors in n-th composite.

%e a(1)=2 (4 = 2*2);

%e a(2)=1 (6 = 2*3);

%e a(3)=3 (8 = 2*2*2);

%e a(4)=2 (9 = 3*3).

%p A020639 := proc(n) numtheory[factorset](n) ; min(op(%)) ; end proc:

%p A166948 := proc(n) c := A002808(n) ; smpr := A020639(c) ; for p in ifactors(c)[2] do if op(1,p) = smpr then return op(2,p) ; end if; end do: end proc:

%p seq(A166948(n),n=1..120) ; # _R. J. Mathar_, May 21 2010

%t FactorInteger[#][[1,2]]&/@Select[Range[200],CompositeQ] (* _Harvey P. Dale_, Apr 20 2022 *)

%Y Cf. A002808, A020639.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Oct 25 2009

%E Entries checked by _R. J. Mathar_, May 21 2010