A091371 - OEIS

%I #11 Oct 29 2013 12:27:53

%S 1,1,2,0,4,0,6,-1,1,0,10,-1,12,0,1,-2,16,-1,18,-1,1,0,22,-2,3,0,0,-1,

%T 28,-1,30,-3,1,0,3,-2,36,0,1,-2,40,-1,42,-1,0,0,46,-3,5,-1,1,-1,52,-2,

%U 3,-2,1,0,58,-2,60,0,0,-4,3,-1,66,-1,1,-1,70,-3,72,0,0,-1,5,-1,78,-3

%N Smallest prime factor of n - number of prime factors of n with multiplicity.

%C a(n) = A020639(n) - A001222(n).

%C a(A091375(n)) < 0. a(A091376(n)) = 0. a(A091377(n)) > 0.

%H Harvey P. Dale, <a href="/A091371/b091371.txt">Table of n, a(n) for n = 1..1000</a>

%p with(numtheory); A091371:=n->`if`(n=1,1,min(op(factorset(n)))-bigomega(n)); seq(A091371(k), k=1..100); # _Wesley Ivan Hurt_, Oct 27 2013

%t Array[FactorInteger[#][[1,1]]-PrimeOmega[#]&,80] (* _Harvey P. Dale_, May 25 2012 *)

%Y Cf. A091372, A091373, A091374.

%K sign

%O 1,3

%A _Reinhard Zumkeller_, Jan 04 2004

%E Definition clarified by _Harvey P. Dale_, May 25 2012